{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Autoregressive Process - Time Series "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from statsmodels.graphics.tsaplots import plot_pacf\n",
    "from statsmodels.graphics.tsaplots import plot_acf\n",
    "from statsmodels.tsa.arima_process import ArmaProcess\n",
    "from statsmodels.tsa.stattools import pacf\n",
    "from statsmodels.regression.linear_model import yule_walker\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simulate AR(2) process "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "ar2 = np.array([1, 0.33, 0.5])\n",
    "ma = np.array([1])\n",
    "\n",
    "simulated_AR2_data = ArmaProcess(ar2, ma).generate_sample(nsample=10000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x540 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=[10, 7.5]); # Set dimensions for figure\n",
    "plt.plot(simulated_AR2_data)\n",
    "plt.title(\"Simulated AR(2) Process\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1.00000000e+00 -2.18875014e-01 -4.86122824e-01  1.10137268e-02\n",
      " -1.24939438e-02 -1.40702356e-02 -5.59697789e-03  3.40084489e-03\n",
      "  1.03671122e-02  8.56304551e-03 -5.91414363e-03 -1.11154970e-02\n",
      " -2.01279061e-02 -8.51705496e-03  5.53189647e-03 -5.09921751e-03\n",
      "  3.37947692e-03  2.55858941e-02 -2.34499218e-03 -1.47326973e-02\n",
      "  9.42860898e-03  3.94645665e-04  5.35446577e-03  8.43422917e-03\n",
      "  5.21493133e-04  3.01655449e-03 -4.73776233e-03  9.35890520e-03\n",
      "  4.73512381e-03 -6.51736824e-03 -6.84934482e-03 -5.31686109e-05\n",
      "  9.25729696e-03  4.56871383e-04  1.09987728e-02  1.53870029e-02\n",
      " -9.84462743e-03  2.20240877e-02  6.15006740e-03 -1.66767903e-03\n",
      " -9.24028046e-03]\n"
     ]
    }
   ],
   "source": [
    "pacf_coef_AR2 = pacf(simulated_AR2_data)\n",
    "print(pacf_coef_AR2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_pacf(simulated_AR2_data);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_acf(simulated_AR2_data);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "rho: [0.32522028 0.48602071]\n",
      "sigma: 0.990741726628625\n"
     ]
    }
   ],
   "source": [
    "rho, sigma = yule_walker(simulated_AR2_data, 2, method='mle')\n",
    "print(f'rho: {-rho}')\n",
    "print(f'sigma: {sigma}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Simulate AR(3) Process "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "ar3 = np.array([1, 0.33, 0.5, 0.07])\n",
    "ma = np.array([1])\n",
    "\n",
    "simulated_AR3_data = ArmaProcess(ar3, ma).generate_sample(nsample=10000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 720x540 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=[10, 7.5]); # Set dimensions for figure\n",
    "plt.plot(simulated_AR3_data)\n",
    "plt.title(\"Simulated AR(3) Process\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_pacf(simulated_AR3_data);\n",
    "plot_acf(simulated_AR3_data);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "rho: [0.33779294 0.50385558 0.06716275]\n",
      "sigma: 1.0002359936664298\n"
     ]
    }
   ],
   "source": [
    "rho, sigma = yule_walker(simulated_AR3_data, 3, method='mle')\n",
    "print(f'rho: {-rho}')\n",
    "print(f'sigma: {sigma}')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Project\n",
    "### Johnson & Johnson quaterly earning per share modelling"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>date</th>\n",
       "      <th>data</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>0</td>\n",
       "      <td>1960-01-01</td>\n",
       "      <td>0.71</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>1960-04-01</td>\n",
       "      <td>0.63</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>1960-07-02</td>\n",
       "      <td>0.85</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>1960-10-01</td>\n",
       "      <td>0.44</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>1961-01-01</td>\n",
       "      <td>0.61</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         date  data\n",
       "0  1960-01-01  0.71\n",
       "1  1960-04-01  0.63\n",
       "2  1960-07-02  0.85\n",
       "3  1960-10-01  0.44\n",
       "4  1961-01-01  0.61"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_csv('jj.csv')\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 1080x540 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=[15, 7.5]); # Set dimensions for figure\n",
    "plt.scatter(data['date'], data['data'])\n",
    "plt.title('Quaterly EPS for Johnson & Johnson')\n",
    "plt.ylabel('EPS per share ($)')\n",
    "plt.xlabel('Date')\n",
    "plt.xticks(rotation=90)\n",
    "plt.grid(True)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>date</th>\n",
       "      <th>data</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <td>1</td>\n",
       "      <td>1960-04-01</td>\n",
       "      <td>-0.119545</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>2</td>\n",
       "      <td>1960-07-02</td>\n",
       "      <td>0.299517</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>3</td>\n",
       "      <td>1960-10-01</td>\n",
       "      <td>-0.658462</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>4</td>\n",
       "      <td>1961-01-01</td>\n",
       "      <td>0.326684</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <td>5</td>\n",
       "      <td>1961-04-02</td>\n",
       "      <td>0.123233</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "         date      data\n",
       "1  1960-04-01 -0.119545\n",
       "2  1960-07-02  0.299517\n",
       "3  1960-10-01 -0.658462\n",
       "4  1961-01-01  0.326684\n",
       "5  1961-04-02  0.123233"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Take the log difference to make data stationary\n",
    "\n",
    "data['data'] = np.log(data['data'])\n",
    "data['data'] = data['data'].diff()\n",
    "data = data.drop(data.index[0])\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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hhBBCCCG9iYhMVfsZo5WEEEIIIYQQssWgkCOEEEIIIYSQLQaFHCGEEEIIIYRsMSjkCCGEEEIIIWSLQSFHCCGEEEIIIVsMCjlCCCGEEEII2WJQyBFCCCGEEELIFoNCjhBCCCGEEEK2GBRyhBBCCCGEELLFoJAjhBBCCCGEkC0GhRwhhBBCCCGEbDEo5AghhBBCCCFki0EhRwghhBBCCCFbDAo5QgghhBBCCNliUMgRQgghhBBCyBaDQo4QQgghhBDSVeQKRbeX0PVQyBFCCCGEEEK6hpmlNJ7wzm/g8KlFt5fS1VDIEUIIIYQQQrqGc0spZAtFnJxfdXspXQ2FHCGEEEIIIaRryOR1rHIlU3B5Jd0NhRwhhBBCCCGka0jntIBLZvIur6S7oZAjhBBCCCGEdA3GkVulkKsJhRwhhBBCCCGkaygJuSyjlbWgkCOEEEIIIYR0DSZaSUeuNhRyhBBCCCGEkK5hrdkJhVwtKOQIIYQQQgghXUPGNDthtLImFHKEEEIIIYT0KOeX0/j1zxxCIp1zeykl6Mg1BoUcIYQQQgghPcq9U4v4xkPncWQm4fZSSqw5chRytaCQI4QQQgghpEdJWaIp0UXu19r4AUYra0EhRwghhBBCSI+SznXfzDZ2rWwMCjlCCCGEEEJ6FOPIraS7RzRxIHhjUMgRQgghhBDSoxj3q5saixghl8wVUCwql1fTvVDIEUIIIYQQ0qN0o5Aza1JqzTEk66GQI4QQQgghpEdJZbs3WgkwXlkLCjlCCCGEEEJ6lHS++xy5TH7NhVvlUPCqUMgRQgghhBDSo6Sy3Td8O5OjI9cIFHKEEEIIIYT0KN3oyKXzBQR9WqZQyFWHQo4QQgghhJAeJd2NNXK5IkYiAQDAarZ71tVtUMgRQgghhBDSo6S6sGtlJl/EcNQSchnWyFWDQo4QQgghhJAepVvHDwxHggAYrawFhRwhhBBCCCE9SirXhc1O8mvRym5aV7fRFiEnIs8XkSMickxE/qDG/V4qIkpErm/H8xJCCCGEEEKaJ2M5cquZPJRSLq9Gk8kXMBTWQi7J8QNVaVnIiYgXwMcA/CyAKwG8QkSudLhfDMCbANzV6nMSQgghhBBCWsfUyOUKqmwQt1sopZDOFRENehHweRitrEE7HLknAzimlHpcKZUF8HkAL3a433sAfBBAug3PSQghhBBCCGmRdK4Aj+j/3w0xxmxBi8mg34to0MeulTVoh5DbBeC07b/PWLeVEJFrAOxRSv1nG56PEEIIIYQQ0gZSXdZYxLiCQZ8HkaCXXStr0A4hJw63lQK2IuIB8GEAv1v3gUTeKCKHROTQ7OxsG5ZGCCGEEEIIccLEGEetVv+JLpglZ7poBv1eRAK+rhCX3Uo7hNwZAHts/70bwLTtv2MArgLwXRE5CeCpAG52aniilPq4Uup6pdT1Y2NjbVgaIYQQQgghxAnjfo3FtCPXDdHKTM7uyDFaWYt2CLkfAbhURC4RkQCAlwO42fxQKbWklBpVSk0qpSYB3AngRUqpQ214bkIIIYQQQkgTpKyOkKNRS8h1gSNnxGXI70U4wGhlLVoWckqpPIDfAvANAI8A+KJS6iER+RMReVGrj08IIYQQQghpP+m8EXI6WtkN7lcpWunz6GYnXeASdiu+djyIUuprAL5Wcds7q9z3Oe14TkIIIYQQQkjzGEfORCu7oUbO3uwkzBq5mrRlIDghhBBCCCFka5G26tFK0couEE0ZyyUM+b2IBr1Y5UDwqlDIEUIIIYQQ0oOYYeBDkQBEumT8gK3ZSdiKViql6vxWb0IhRwghhBBCSA9i6tHC1vDt7ohWmho5vaZ8UZWGhJNyKOQIIYQQQgjpQYyQC/m9iAV9XRKtNF0rPYgEvADAzpVVoJAjhBBCCCGkBzHRyr6AV89s6wIhZx8IHg7qvozdsK5uhEKOEEIIIYSQHsQ0Own5vIiGusuRM+MHgO4Yi9CNUMgRQgghhBDSgxhHLhTwdE+NXK58IDjAaGU1KOQIIYQQQgjpQTI5e6v/LotW2h25LlhXN0IhRwghhBBCSA9iBoL3WUKuW6KVHgF8HkE4QCFXCwo5QgghhBBCepB0vgCfR+D3enSNXDdEK/MFhPxeiIitRo7RSico5AghhBBCCOlBUtkiQn5dhxYN+rCSdX/4diZfRNCnJUokaGrk3BeY3QiFHCGEEEIIIT1IKlcoE3JKAUmX3a90roCgT68pwq6VNaGQI4QQQgghpAfJ5AoI+bUciIa0aHK7Ti6TLyJorSno88DrETpyVaCQI4QQQgghpAdJ5QroszlyAFwfQZDJFRGyHDkRQTjg5fiBKlDIEUIIIYQQ0oOkK6KVgPv1aOl8oeTIAeiasQjdCIUcIYQQQgi56MgVilhK5txeRlfj5Mi5Hq3MrTU7AaAdOdbIOUIhRwghhBBCLjo+cdsJPO/D33O9C2M3k84VEQqUNxZxPVqZX3MJAePIMVrpBIVcF5MvFDEdT7m9DEIIIYSQLceZxSQuJDJYStGVq0Y6V0DIcr9ioS6JVq5z5BitrAaFXBfznw+cw3P+4rtYWM26vZSuplhU+NxdU0jnuFtDCCGEEI2JCE7H0y6vpHtJ5QroC3RZtDK/Nn4A0E4hB4I7QyHXxcwmMsjmi3h8dsXtpXQ1j84k8PYvP4hbHznv9lIIIYQQ0iWsWBHBmWWmm6qhHTlLyHXh+AEAiAa9dOSqQCHXxWTyevfh5HzS5ZV0N0mrAHZ+hc4lIYQQQjQJ6+L/3BIduWqksmuOXNDnhd8rrgs5Ha1cc+TCQV/pWo+UQyHXxWTzRQDA1PyqyyvpblJWpJIRVEIIIYQYSo4chVxV0uvcL1/pfXMLHa2sWBMdOUco5LqYjCXk6MjVJmXlpheTFHKEEEII0azQkatJoaiQzRdL4wcAHa90WzRl8sWyrpXhgBfpXBGFIruPVkIh18Vk6Mg1hHHk5unIEUIIIcTCCJJucuQKRYW5lYzbywCwVsJjF3KRgLtCrmiJy0pHDgBnyTlAIdfFZAtayJ2YW+UMlBpkcvp9WqSQI4QQQoiFiQhOL3VPs5Ov3D+NZ37g210xEsEkmuzuVyzkbrTSXPva457hQHeMRehGKOS6GCNQEuk84kn3P/DdCmvkCNEUiwo/PrPk9jIIIcR1MvlCSRTMLKW7ZkN8aj6JdK475gSb66e+iuHbbjpy5to3VDZ+QP9/DgVfD4XcJnDo5ALm22CbmxMQAJxkvLIq5kTEGjnSLV/UbvH9x2bxwo/+AI+cW3Z7KYQQ4irGVdoz3IdktoBllxt4GMy1yoWE+/HKdG69+xUJujt8O23FPSsbsAB05JygkGszxaLCqz5xF/7pjqmWHyuTKyDg1X+iKTY8qYqJBiysZnv+Qr6XeeTcMg7+0dd7uqbUXBhQyBFCeh3jKl06HgPQPXVyJlJ5Ydn99aQdHLlYyFca2+AGxpErGz8QYI1cNSjk2sxKNo9MvtiWfHG2UMQloxGI0JGrhdm9yRWU652WiHvcdzqObL6IE3O9+1lJWOedYxdWXF4JIYS4izkfXjoeBQCc65I6ue5y5NbXyLk9fsA0YAk5OnKMVlZCIddmlqxatmyh9YMtkyuiv8+HHf0hOnI1SGfX3uvFVdYS9irmM9It8Rk3SKT18U8hRwjpdczG7gFLyHWLI2d6Hsx2gZAr1cgF7PVoPqRyBdda/aedHDmrRo5DwddDIddmjGVurOFWyBaKCPg8mBiJtOzIff3BGTxwJt7ymroRcyICgAXWyfUsJlJpxEwvYnZRj89SyBFCehtzPtw/HoVI98ySi5ccOffXY0RTZbMTAK4lnIwj5zR+gKmr9VDItRmz02JmwLWCnqPhxeRouCVHTimF3//3B/CJ2060vKZuJGUTzQur7u9wEXcoOXKp3j3RmyjR1HwSuULr5yBCCNmqmIv+wT4/xqLBrolWxks1cu5fr6Ry62OMsZDbQs7qWlkxEBxgsxMnKOTajHHksm0Qcpm8bnYyMRLBwmoWy006DeeXM1hK5cqcq4uJdK6AiPUhX2C0sidRSuHUghZyvezIJTL6teeLqqebvhBCiGnYEQ35sGMg1BWOXLGo1pqddEG0Mu0wRy5i3C+XyhScHLm1OXIX53VsK1DItZl4Slvm5kBshWy+iKDfg8mRMADgVJOu3JHzCQBrRa0XG+lcAbuG+gBwKHivMr+aLe0eNrvhcTGQSOdLX36skyOE9DJGiMSCfmwfCHVFjdxyOgelgIDXgwsJ92fbpfPOzU4A9xw5p5EIXo+gz++lI+cAhVybKdXItcWRK5YcOaD5zpVHZnQr8otVyKWyBYxGg/B7hTVyPYo9epzo6WYneVy1awAAcHyWjhwhpHdZyeTg9QhCfg92DPR1hZAz5Tf7xiJI54qutvkH1sY3VY4fANyvkbMPBAes+XbZi/M6thUo5NpMO6OV2bxpdqIduWbr5I7M6J35dBsasHQj6XwBfX4vhsIBLKxQyPUipxa0aIkEvD0u5HLY3h/CzoEQHTlCSE+zks4jGvRBRLB9IIREJu969N6MHrhsm55t53adnLkuLHfk/ABcjFY6OHIAEA3SkXOCQq7NLLWx2UnGanYSDvgwHgviZJPzsY6cb58jt5LJ40O3HG2LUG0XqWwBoYAXw5EAHbkeZWo+CRHg8h39WE71drQyFvJh/3iUQo4Q0tMkMvlSTHDHQAgAcN7lIdym0cnB7ZaQc7lzZSqnezF4PVK6LRJ0t7GIuVYNVjhy4YCP4wccoJBrM2vRyvbUyAWsepfJkUhTjlyhqPDYecuRa8OafnhsDh/51mO4+8RCy4/VLtK5IkI+LeRYI9ebTM0nsXOgD6PRQE87civWhcv+sSiOz66g6NIcIEIIcZsVa2MLAHYM6Dp6txuemNEDZki527Pk0rlCWcdKQNcUAnAt9mmMEHuzE8AaVE5Hbh0Ucm3G5J9bdayUUsgWiqUDeWIk3FSN3NT8KjL5IkJ+T1uilWanZGqhe+pvUrkC+gIeDNGR61mm5lexdziMWMjfs81O8oUiktkCYiE/DoxHkcwWMOPy7jMhhLjFioMjdy7utpDT308mWtkdQq6yFk3/t3tdK52FXDjoRZI1cuugkGsz7Wp2Yn6/5MiNRnAhkdmwrXzU6lj5hJ0DbYlWloRcC3Pt2k06p2vkhsMBLNCR60lOLSQxMRJGLOTrWUfO7FTGQj4csHZ7Ga8khPQqK5k8opYjN94fBOC+I7doCbndQ30I+jyujyDQG+HlQs7n9SDk92DVpRhjOleAzyPwecslSoSOnCMUcm2mXc1OsoXyHYlmG548OpOACPDEXQOlAtJWMB2OTjRZr9dulFL6ROTX0cqlVA55DkLuKVYyecytZLF3JIz+kB8rmTwKPRgpNAI2FtLRSoBCjhDSu5hmJ4CutxqNBjCz7O5Q8KVkFv0hH3xeD8b7g7jgcmoinSus6w4J6IYnbm2K6v4Q6+VJJMBmJ05QyLWZtjlyuXIhN2mNINjokN+j5xOYGA5jKBxAtlBs+QI3bb2ubhk2nMkXoRQQtIScUmt/A9IbmGNxciSy1ja5B105u5AbjQYw0OfH8VkKOUJIb5LIrNXIAcD2LhgKHk/lMBgOAADGY6EucOSKCAXWC7lYyD33K5NfH/cEtCOX5EDwdVDItZFcoVg68FttdmIcOROt3Gs5ciebcOQu2xYrFbO2Gq+0Ryu7oZGCWU+f34uhiD45LrJOrqc4ZX0m9g6H0d+ni7R7sU7OtNWOhfwQERxg50pCSA9jd+QAYHu/+7PkFpM5DIX199R4LOi6kNOOnIP75WKr/3TO2ZGLBn1YzeZdH6LebVDItRHT9nw4EkCuoFoSOpmK9qv9IT9GIoENOWHpXAEn51Zx+fZYaXejVSGXsn4/ky/ivMttc4G1GSh9AV0jBwDznCXXU0wtaCE3MRJGv7X72ptCbs2RA4ADVudKQgjpNfKFIlK5QmkmGqAbnrjtyC0lsxgoOXLdEa2srJEDrA6RbkYrHRy5cMCHorp4ZyI3C4VcGzHzQcZjuqg220KtVqUjB1idK+cad+SOXVhBUQGXbbc5cm2KfALY0Fo2i5TNkRumI9eTTM0nMRwJIBbyoz9ktU3uwWilSQOYHej94xHMrXbGnBwAACAASURBVGRL7a4JIaRXWLUieFFbtHLHYAhLqZyrs8jKHLn+EJbT+bY0omsW0yyukmjQ7974gVyhiiNnddNknVwZFHJtxNRmjVlCrpXmIlmH9qt6llzjjpzpWNlORy6dK8DMjWxmHEK7Mc1XQn5PScgtrPaeG9PLTM2vlpoBxSwh14tDwe3RSgClzpV05QghvUYiY50PbdHK0ggCF125eDKLQasEwFwrujmCIOUwfgDQosm1aGUNRw4Ah4JXQCHXRpastrLb+vXJIlNoXjRVjh8AgImRCKaX0g2LsSMzCQS8HkyMREoRzXZEK3cN9cHvle4Qcjkj5LwYtHa56Mj1FlPzSUwMGyGnT/S96Mgtr4tW6jlFrJMjhPQapYRCqLxGDoBrdXL5QhHL6byt2YkWchdcLFNJZYvOQs7NZidVHLmIJcrpyJVDIddGliqile1w5AK2ORqTo/pi9fRCY5HGI+cT2D8ehd+aCQK0ni1O5wqIBHzYMxzGVBdEKzO2aGXI70Uk4GWNXA+RyRdwbimFvVZX115udrKSycPvldIX4K6hPgR8Hgo5sqX4/N2nSg2MyNbi1HwSD5yJu70MAGudi6Nd5MiZzbbBUrMTvZ4Ly+45cplcoXR9aCca9LtaI+fctVLftsrOlWVQyLURU4tSila2UI9mul7a7eUJ62K10c6VR2YSOLhNx6vMhyLTcrRSW96TI5GucuRMse5wNEBHroc4s5hCUYGOHHS00nSsBACvR7BvNEIhR7YM6VwBf/ClH+PTd5x0eymkCf7im0fw2k/9qCvmeCacHDlLyM0suTNLzlyblIRcv3Hk3I1WOtfIeZEtFFvuwN4M6TqOnFuDyrsVCrk2spTSB5fZZWllKLijI1caCl5fQC2lcji3lMbB7f0A1oRcusUPpf7Qe6x6vaTrbWDt0UoAGA4HsLBKIdcrmJ1741b7vR70+b2lerFeIpEun5kE6Dq547Pub7gQ0gjm3P34HI/ZrcjCahYLq1nce2rR7aWU3CR7jVzI78VQ2O+aIxe3ym9MtHI4HIDXI65FK3OFIvJFVaVGzhJNLrhf2aoDwc2aKOTsUMi1kaVUDtGgD2HLHWplJ8O4eUGb5T0Y1kN+G3HCTKOTg9u1I2d2XFLZVrtW6sLYydEwUrmCq0W6gG38gPX6hiJ05HoJs6mxdzhSui0W8mE51Xsn+mpC7vRi0tWuaIQ0SknIsUHPlsRsoN368HmXV+JcIwcAOwbcmyW3lLIcOasEwOMRjEYDrkUr7XN4K4laTbPciFfWi1ZyKHg5FHJtJJ7KYqDPX9pJaC1aud6RA7QrN9VAtPLIjBFyxpFr10DwIkI+bynmecLlnVMnR66VGrl7phbw5cNn2rI2svlMLSQRDngxGg2Ubuvv85c6lvUSlcNvAWD/WBRKAY/TlSNbALMJd3ox1VKihbiDibTf8kgXCDmHGjlA18lNuyTkFq2O2kPhte+r8VjItWil2QgPOc6R07e58V1aLVoZZbMTRyjk2shyKqeFnCWa2hGtDFYUoU40WJt2ZCaBWNCHnVYmvK3RyoDXFvN0tyg9bRs/AOhh7K04cp+47QTe97VH27I2svlMzScxMRIp1YUBvevILVs1cnY4goBsJYwjVygqnFrg5sNWYzmdR9DnweOzq66fc8zFvonjGbYPhFyrkTOzhk2NHGANBXdNyFnXT46iSa/RjWhlJl8sdVq3w/EDzlDItZF4MofBsB8Br4lWtu7IBb3lB/PkSBhnG9itPHI+gcu2x0oXuKHS+IHWu1aG/B7sGuyDz+P+CIJKR24oEkAyW2jaeTy3lO7J+qqtytT8aqnRiSEW8vfk39ApWnnJaAQe4QgCsjVYtNU3s7Zz65FI5/C8K7cBAL7lsiu3ktEJBY9Hym7fMRDCYjLnStw8nsxCBOi3bbiN9wcx61KNXGWzODsmkrrigiOXyTt30gz4PAh4PVhhtLIMCrk2srQJjlzAt96RKyrgzGJ1J0wppTtWbo+Vbgu2LVpZQNDnhc/r0SMI3HbkcgX4vQK/d82RA5qfJTezlEY6V0Su0D2xni8eOo2f+fD3XW8s020UiwqnF1OlYeCG/pCv1Oa5l1jJ5MsK+wG9wbFnOIxjPeTIHTq5gCe96xv4nc8fxt0nFvi52UIsJtcuGhkH3lpk8gVk8kVcvj2GK3f049aHL7i6HqeoOQBsH3Bvllw8qa8R7eJyLBbC/GoWeReuOdYcuerNTjrdAbpQVMgVlKMjBwDhoJeOXAUUcm0kntKO3FqNXCvNTvTvVgo5052vloC6kMhgKZXDwW02IefzQKQ94wfM7s3ESLgrHDl7UazJnjdTJ5cvFEvdo7qpff03H5rBkfMJJLPchbIzs5xGNl/E3hE6ckopLeQqopWArpM73kOO3MPnlrGczuOWh8/jZX93B5734e/jkz84gaVkbx0TW5HFZBaDYT9Go0E2PNlimO/MWMiPm64Yx6GphTKHtdOsZPLrGp0A7s6SW0xmy+rjAB2tVAqYc2H+bSpbw5FzqWvl2ugtZ3kSCbg3qLxbaYuQE5Hni8gRETkmIn/g8PO3iMjDIvKAiHxLRCba8bzdhFIKS6kc+vv8JfHVSrQymy/C5xF4K2IBa7PkqguoR0uNTtaEnIgeFJxuYU2FokK2UCzt3kyORHBybtXVHe90hZAbiTbvyM2uZGDG33SLEFBK4b7TesCqGThPNOYzMDkSKbu9v6/3HLlktoBCUa2LVgK6Tu7xudWumO3UCUyL7zvfdiM++NInIRr04U/+82E8+X234i1fvA/3TNGl61YWVrMYDgewbyzCEQRbjDUh58NNV25DUQHfOeKeK5fIVHPkrFlyy52vkzOpLTvjMTNLrvPC0lwPOg4EdylamTENWBzq9gDduZLjB8ppWciJiBfAxwD8LIArAbxCRK6suNthANcrpZ4E4N8AfLDV5+020rkisvkiBvsCJUu4lWhlpsocjZFIANGgr6Yjd9QIOZsjB+iYVSvRSrNTYj70EyNhrGYLruwkGVLZ8mGWZrermVly0/G1E2m3OHJnFlOl95dCrhwzQ27vcGW00o9svthTLfertdoGgANjUWTzxZpx7IuJxWQWsaAP/SE/Xnb9HvzHbz4DX33TM/HS63bjmw+dxy/93zvw/L+6Df90+0lX4kykOovJLIYiAewfi9CR22KYzc9YyI+rdg5gW38Qt7pYJ7eSzjlubLntyNkbnQDAeL9ejxsjCFLZ8h4DdsJ+L0Q6P35gbfSWc7QyEvQxnVRBOxy5JwM4ppR6XCmVBfB5AC+230Ep9R2llLmKuBPA7jY8b1dhLrIHyhy55g+2bL64LlYJaGetXqTx0ZkExmNBDEXKLfw+v7f0wW2GShveOCGNDCjfLNK5YpmQK9XINSHk7Jn55S5x5A5bbhxAIVfJ1EISfq9g52Bf2e39IXey/W5iv4iqZL/VubJXGp4sJXMYqLhYesLOAbz3F56Iu952I97/i09EwOfBH9/8ED531ymXVkmcWFjNYSgcwL7RKBaTOVejeWRjmPNtf0g3GLnxim343pHZlq6DWmGliiMXDvgw0OfHubg7NXJO0UoArnSuNH8bpzlyHo9YMcbO/v3MBqyTkQHoyCejleW0Q8jtAnDa9t9nrNuq8XoA/9WG5+0q4mbQo71GroUOkdkq7VcBLaBqOnLnyxudGEJ+b0vRypINb6KVoybm6d5OfypXKJuBMtDnh0eac+TO2VoSd4sIOHxqsfT/KeTKmZpfxe6h8Lr4sREz3SLGO8GyLdZUyYGx3hJyTrvehkjQh1c8eS++8tvPxO6hPtz5+HyHV0dqsbiaxXDEj31j+ruF8cqtw3KqfDPpeVdsw2q2gDsfX3BlPdWanQDalXPDkTPNTuyMRt2LVtZy5AAjmjocrSzFPas0Owl4ORC8gnYIOXG4zbEAQUReDeB6AH9e5edvFJFDInJodna2DUvrHKaQfqDPD59H4BEg20JsJ5MvODpygI40nllMOsaCCkWlhdy29UIu6PO0FDcr7ZRY0cpdg33wesRVRy6VK5Rlqb0ewWA4gIUmauTsjlz3CLl4aRYghVw5eoZceN3tsZ505NZ2wysZsJpHuD3XqVPEU+t3vZ24bmII955aZL1cl6CUKkUr91mbD4xXbh0SFZtJT9s/gj6/17UxBIkqzU4Aa5Zch2vkcoUiVjL5deemgM+D4UjAFUeuNH6gmpALdd79KjU7qVojR0euknYIuTMA9tj+ezeA6co7ichNAN4O4EVKKccjVin1caXU9Uqp68fGxtqwtM4Rt0UrRQQBn6e1ZicF52gloIVcrqAcd5ROLSSRyRdxWTVHrgUhV4pWWh/6gE/Pkzvh4q5p2hpQbmco7Mfi6sZFz7nlNIasnfxuaHaSyRfw8PQynn1QfxaWKeRKKKVwaj65boYcAPRbO5699H6ZOgYzxLWSA+ORnnHknHa9nbh27xDOL2dwNu7OcGBSTiqn29cPhQPYM9QHv1foyG0hTALCzEgL+b141qWjuPXh8x3fLCl18a3hyHV6/MCSwzBww3gs6EqNnJkrXM390qKp09FKq0auSiItEvBx/EAF7RByPwJwqYhcIiIBAC8HcLP9DiJyDYC/gxZx7g4X2STsNXKAPghbafWfyTk3OwFqd648MrMMALjcUch5Wop7rjU7WfuATYy4O0sunSus200ajgSailbOLKVx6bh+37rBzXl4ehnZQhHPunQMInTk7Cwmc0hk8thb0bES6FVHzsSanC9cDoxHcezCSk+4T3GHFt9OXDcxBAC491S8zj1JJzDn7OFwAD6vB3uHw3TkthDmfGt3wW66chuml9J4+NxyR9eSzBaglHPzJwDY3t+HuZVsR+v34sm18ptKxmLuDAVP1alHiwV9WOnwpnbd8QNBX8dHInQ7LQs5pVQewG8B+AaARwB8USn1kIj8iYi8yLrbnwOIAvhXEblPRG6u8nBbllK0MmyEnKelaGUtR25ypHpt2pGZFYigJEjs6Bq5VqKV63dvJkciODnv3giCVBuF3Ll4CruH+9Dn93aFm2PGDly7dwj9IT+FnA2zieHoyIW6x1XtFJWxpkr2j0WxnM672mG2ExSLegxMtRo5O5dvj6HP78W9U4t170s2H5OiME269o1FORR8C5GwatLsNcvPvXwcIuj4cPBSF98qCYUdg53vFGnGogw6bDKNx0LuNDvJFRD0ecoGlNtxo7HI2viBao6cF9lCsaWu8BcbbZkjp5T6mlLqMqXUfqXUe63b3qmUutn6/zcppbYppa62/r2o9iNuPZZSOXg9UrLyA74W3a8ajtx4LIiQ34Mph9jJkfPLmBgOOw54DPnaG60EdMOTRDqPRZeG7aayxXVtaocjG6+RKxQVzicy2DEQQizk6wo35/CpOHYMhLB9IISBPgo5O2b0wORo9Rq5Xmp2ksjkIaJjJ04c6JHOlYl0HkXlfLFUic/rwZN2D+DeU90j5B44E+9op8bbj891zQWROWcPR/TF974x3dSrV+YfbnWWHdr9j0aDuHbvUMfHEDi5g3bcGEFgrpGGnKKV/UHMJjIodvhYTzmUpthxw/1KN+DIAWC80kZbhBzRQq4/5IOI3tkI+jzItNLspFBEoMqOhMcjmBiOVHHkErjModEJoKOV6RbEZbpijhwATFrNJmqNQ9hMnKKVQ+EAFlezG3IJ51YyKBQVtg/0ob/Pj0SHOzU5cd/pOK7eMwgAFHIVTM0nIQLsHlov5CIBHzzSe9HKaMBXdWe1JOQu8qhaqXtwAzVygI5XPjy93BUzB3OFIl72d3fgY9851pHnO72QxCv//i786z2n69+5AxgBa2Kx+0ejyBZ6Z/7hVidRZW7bjVeM48dnlzpak2ZcpFo1ckB5p+rNphSt7HNy5ILIF3Wzn07idP1kR29quzMQvHqzE71eNjxZg0KuTcRTubJdYF0j1+r4gep/Hl2bVi6e0rkCTs4nHevjAD3/LdVS18r10cpSvV4TRenvuvkhvPsrDzW9Hr2mAvoC5e/TcCSAfFEhsYEPutmZ29kmRy6TL+D5f/X9pjt2za9kcGohiWv2Usg5MbWwiu39IccibY9HEA36uiIe2ykS6XzVWCUAbO8PIRLw4vhF7sgtJqs3FHDi2r1DyBcVHjiztJnLaohTC0mkc0UcOZ/o2PMBwP2nu6NGsFQjZ0UrLzEjCBiv3BLoc9D6z93zrtgGAPjWo51z5Uzzp0gVIbd9QM8e7aQjF68ov7EzHrOinh2OV6ZyxaqNToC1aGUnS2fqjR9Yc+Tc33zrFijk2sRSKlfqlgdY0coW6tFqjR8AdKRxaiFZZsUfn11BoagcO1YCWly2FK3MrW92sme4DyIbnyWXLxTx7/ecwT0t1KfkCkXki2pdltpcCCxsoB5oxtqZ2z4QQizkL83lapa5lSwenUng8z9qbrfb1MddvUc3ZKCQK2dqPom9DvVxhljI33OOnNNFlEFEsH88etGPIFhrKFA/WgmgtFHSynmoXRiR3SnhYrp1Pni2s40oqhFPZuGRtRrXfdac0ov9mL1YSKTzjuNPDoxHMTESxq0Pd1DIWYmaanPkokEfYkFfR13CeCoLr0cc36PxfneGgqdzhZpCLhL0oajQkgHQzJqA2uMHADpydijk2sRSMlsW5wn6PC3VHmTzRQS9tR25bL6ImeW1E9GRGb2TW82RC/lbcwkzufXRyqDPi50DfRueJffg9DISmTxWW/gwlmagVI4fMEJuAzEFszO3Y6CvLXEC4wb94LG5psTz4VNxeD2CJ+4aAKBb6veSw1SPqflkqemPE/19/p6qkVupMTPJcGAsetHXyNVq8e3ESDSIS0YjXVEnd9wScGfjqY7Uf5yL63Pe0fOJjnbvq8ZCMovBcKAUDx6OBDDQ5+cIgiqstPj92W6Wq2wmiQhuumIbfnh8vmPrrdf8CdCbtp2MVi5aY1FM+Y2d8Zgl5JY727lSC7nq15nmO6WTosk4crXGDwDgUHAbFHJtYilVPrso6Pe2NEcuky9WLfYE7J0r177kjpxPIOD1lOKOlYT8upNms8XjptlJ5Q7OJaPO9Xq1uP34HIDW7PG0g0MI6PbVADbUNGBmKY2Az4OhsB/9bYhWmgvKVK5Qeq0b4b7Tcd1VzxKpxpHrhfbx9VjN5DG3ksFeh2HghljI17KrupWoF60EgP3jUZxbSl/UO5mVdVaNcM3eQRzugsHgduepE67ctOXI5YsKR2fcF/iLq7myRhAign1jEY4gqMJvfu5e/Mon73b9uDXUOgfdeMU4svkibnts49+FzbDWtbK2kOukI7eUrN5N17VoZbZOjZxxvzr4XVp/IDhr5CqhkGsT8YqW1wFviwPB80UE6jhyAMpmuB2ZSWD/eBT+Kr9nBE+zu6/pfAE+j6x7fKd6vXrccXweAFraoUtn9fvrNH4AwIZGEEwvpbFjIAQRsWJ5rbk59hjkrY9srPVyoahw3+l4KfYFaCGXK6iORhy6FVPbM1FDyPX3XLTSuT7Fzv4x3fDkYq6Ti6fMUOLaotbOtXuHMLeSLR1XbnF8dgWj0WDp/28200spjEb1ufLBafdrBBdWs6Vzt2HfKEcQVGNqfhWHphbxg2OdEUe1UErVjHffMDmM/pCvY90r69XIAcDOgb7O1silslWbMPUFvIgFfZjtdLQyXztaGXUhxpjO6Wvfao27So4cu1aWoJBrA8WiwvI6R86DbIs1cpVt9e3sGOhDwOspc+SOziRwcFu06u+ErB2OZjtXpqsUxk6ORBBP5kr1KfXI5Av40ckFAGZwZ5MOYTVHrgkhN7OUwvZ+vSsWC/qQzrU2p8TEIK/a1Y9vPXJ+Q6/x+OwKVjL5Un0csDZonnVyKG0aTAzXiFaGeq/ZSa3dZ2Ctc+XFXHMUT+rOeb4am2CVrA0Gdy9eqZTCsQsreO7lY/BIZ8T2dDyFGyaHEQv58OBZ94XcosMg931jEVxIZLj77sC8VQP+19/uTJfTWmTyReQKqqoj5/d68FOXj+Pbj17oyDiJlUweQZ+nZp+B7QMhzK5kkGuhu/hG0I5z9aTAWH8QFzo8FLyeI+dGPVomX6jZ6M+sqZtixW5DIdcGEhk9u6hMyG2yI+f1CPYM92FqTu8iL6VymF5K4+D2/qq/YwRPsw1PUlXy1BOlEQSN7WjfdyqOdK6Iq/cMIl9UTQ9OX6uRK19TOOBFwOfZcI2caUlsvoxaceWM4PrFa3bj/HJmQw0F7julG51UOnL2x+1ljAtdK1rZ39e6q7qVSKRzdV2oiZEwfB65qOvk4g5ioB6XbYshGvTh3in3ujfOrmSQSOdxxY5+7B0Ol+rlNgulFKbjaewc7MNVOwfw4LT7DU+cHLn9VufKE3TlysjkC0hk8tg12Ie7TyzgrsfnXV2PqUfurzH246YrtmFhNYv7Tm/+hkkiUz9qvmMgBKWA8x2qS1tK5Rw7VhrGY8GODigHqm/OG8x72Nlo5frZwHbWopVMJxko5NqA2fmvdOSaFXL5QhFFVT0jbJgciZQcucesltUHt9dw5FoUctU6HF1idRdrNF55+/F5eAR47uXjAJovWq1WIyciGLZmyTVCsahwfjmNHYO6JbGJh7QSzVtO5SACvOjqnRDBhiIlh08vYqDPj0tstY4lIefS4PVuYmohiaGwv+zzVkks5NMbLD0wTDibLyKTL9a9cPF7PZgcjVzUQm6xRh1KNbwewU/sGXC1c+XxC/rceWA8igMd6C4aT+aQyhW0kNvVj0fOLXfMmXBCKYV4MldqVGXYZ8WBH5+7eI/ZZjBpk9c/8xKMRgP4aIdmD1ZjOaW/K2ttJj374Bh8HsEtD2+s1KAZVhpIKGy3Nm47VSfn5DjbGY+FXOpaWaPZiSvRytqOXJ/fC48wWmmHQq4NxEuzi8rnyDUbzTMCsFYsANAz3Kbmk1BK4dEZI+TqO3LN1lllquze7BkO6xEEc405cnccn8cTdw2UTqSrTX4gS46cw5qGIgEsrDYmeuZXs8gVVMmRM7uKLQm5dB6xoA+j0SCu2zu0MSF3Ko6f2DNYlhGnI7fG1Pwq9tboWAloIadU88fWVsI4j/UuXADtcFzU0cqKeZ6Nct3eITw6s+xaXMf8TfaPRbF/LIrH51Y3NYI2bXXr2zUYwlW7BpDNF10V+KvZArKFYlmzE0C7yB7BpjuUWw0Tq9w11Ic3PGsfbntsDoddjAabc1CtzaT+kB9P2TfckTq5Rrr47ujgLLlMvoBktlC1Rg6wHLlEuqPNa+oNBHcjxliv0Z+IIBLwMW5tg0KuDSw5OHKtzJHLNijkJkfDSOUKmE1kcPR8ArGgDzstMeKE2XlptkauWrQy5PdiR3+oIUcumc3j8OlFPG3/qK1otUlHrkoXTQAYiQSwsNrY7pbZkSvVyLUpWmliFDdesQ0PTS831Op4NZPH0fMJXLNnsOz2dgm5e08tYm6ls7t+7WZqPomJGjPkgLVZVL3QudJ8odVrdgJox2dqPumq+7KZVI6BaZRrJoZQVMD9Z9yJVx6fXUE44MX2/hD2j0WRzRdxdnHzWqNPx9fGrTxhpx5x4madXLVuo0GfF7uHwuxcWcG89X6NRgN49VMnMBj246Mu1sqttfuv/dm76YptOHZhBSc2eaREtzlyS8n6Y1HG+4NI54pIdEigKKWsa7r60cpOrQmwDIMqowcM4aCX4wdsUMi1gXjKDKEtnyOXyReb2l2pN0fDMFEaQZDEozMJXLY95jijxFDqWtlCtLLa7s2ELeZZi0MnF5ErKDx9/0jLbWTrOXKLDcYQze602aEzJ69WRIB9HMVNV+gI6bca6F75wJklFBVw9d7NEXK/8g934+Ufv3PL1o9l80VMx1OYrFEfB9jjsVvzdW6ERmYmGQ6MR5Evqg13md0qLCZz61ydRrjWaix0r0vxyuOzq9g3FoHHI9g/vvmDsM2m0s7BPlwyGkE44MVDLtbJmahgZY0cAGsEwcV5vDbLvLUZNxwJIhL04fXPuATfevSCa2K80XPQTVdsAwB8a5NduUQmj2iw9nmgP+RDJODtiCMXT61PbVVSGkHQoTq5rFXCUzmH107Q54HPIx0fP1DLkQO0U7jSA2mbRqGQawNOjlzQ54FSekbPRmnYkTNNRuZWcfR8Apdtcx4EbijVyDU7fqDG7s3kaLihZie3H5+H3yu4fnKoZNs3XyNnjR9wOBENh/0Nd60sOXImWtkGEbCcypUe58B4FBMj4YYiJYetQvCrd5cLuVjIBxG01Ikxmc0jkcnj2IUVvOlfDneke1i7ORtPoahQN1rZ32dc1Yv/ZL9cijU14MiN6XPExVgnVygqLKdzGGgiWjkQ9uPAeBT3nnLJkbuwUhoPsW9087uLno2nEPB5MBIJwOsRPGFnv6uOnGlMVVkjB+j348Tcak/UuzaKiVaOWOMjfvnpk4gFffib77rjypnvyv4656A9w2Fcvj226fHKlUyurqgUET1Lbnnzh4Ibx7mmI2eGgneoc6W5fqpVjyYiiAR9nY1W5op1+0NEAj4kGa0sQSHXBkyNXGW0EkBTDU/qDUQ07Brsg88juPvkAuLJHC7fXk/ItRqtLFZ1CSdHIlhYzdZ1jO44Podr9gwhHPAhbAmwVmvknMTlUCSApVQO+QYiZOeW0vB7BSPWRcRatLI9jpyI4MbLt+H24/N1T4j3nYrjktHIugsaj0cQC/pacuSMsL1hcgjfOTKLD3z90aYfyy2M61trhhywJmrcHkGwnM7hlz95N45dSGzac6xswJHbN2bcnovP4VhO5aAUmopWAsC1ewdxrwuDwZPZPM7GUyUhNxQJYCQS2FSxPR3XXXpNHe4Tdg7g4XPLrm3umAvdYQcRvm8sglSugJkOdRfcCsyvZuH3Smlg80CfH699xiT+68GZUuOzTrLcQI2c4aYrtuFHJxc3td67kWgloFM4Jma8mRhHrmazk34t5Do1Sy5damIrbQAAIABJREFU6vpdO/kVDfo6G62sM9sO0J0rVxmtLEEh1waWUzkEfZ6yg88InmYanjTa7MTn9WD3UF8pplDXkfO11rUykytU/dCbmOepGq7cUiqHH59dwtP2jwBofbDjWtfK9e+TEWWNxCtnllLYbruoMV8A7RJygI5XZvNF3PZY9eGtSikcPh1fVx9nGAj7W/ryW7Sav7zhWfvwy0+bwMe//zj+9dDpph/PDczxVb9Grjscue88egHfPzqLr9x/btOeYyPRyohVR3sxOnKli6VIc0LuuokhxJM5PL7J9TuVmNigEXLm/29qtDKewk4rSg4AV+0aQDJb2PTapWqY87SzI6e/WxivXGN+JYORSLCslOJ1z7gEfX4vPuZCB8tEOg+Rte/0WlyzdxCFotq0ukelVEPNTgCdwulkjVytTstjHY5WpmuUptiJhXwbjlZOza/iZJPnkky+MUeuFxqZNQqFXBuovGgH1ty0ZhqemLlq9Q5mQAso8yV4sK4jZ4RcswPBC6Wh4pVMjppZctU/vHefWEBRAU+3hFzYqpFrdmcllS3AI3CctzdUEnL145XnltLY0b92UePzehAOeFuLVqZzZTN1brhED96tVRswvZTGbCKzrj7OMNDXmpAz8aXhSADv/Pkr8cwDo3jbl3+MQ9Zw9q3A1HwSfX4vxqwYSjVKjpzLNXLfOzoLAJva2j6xgWglAOwfj16cQs46vgf7Nh6tBIBr97pTJ2cEmxnYDui/0Wa6ptPxFHYMrjXGumqX7nb80LQ78crF1Sy8HnFsX88RBOtZWM2WYpWG4YhufHLz/dNNX0Q3S8JywOydlqux19qEO7XQWJfrjWKGkzfmyIVwIZFuKLnTCos1osOG/pAPAZ+nY9HKWokmO5HgxkXTW//tAfzhl37c1Lr0+IEG1sRoZQkKuTYQd5hdVIpWNiGazO/Uc+SAtTq5sVjQsVDczlq0spWB4M4fMHNyrtVE4fbjcwj5PSWh0g5Hrs/vdWzwYiI6jdTJzSynS/VxhljI17Sbk8kXkM4Vy8S93+vBcw6O49uPXqgaXzLto6+xGi9U0qqQK3WGiwTg83rwsVdei91DYfz6Z+7BmcXN+VJtN6cWVjExEq7Z1AdoTzy2VYpFhe8f1Q7s4VOLm3axYJoFNXLhAqA0p+xiqzmKN9AZrhb7x6LoD/lwb4fbuB+fXYVHyuPC+8d0VL3ROt+NkC8UMbOcxq7Btc2rA2NRBH0e/PiMO0JuIZnFUNjv+Lne1h9EJOClI2djzmF4OgD82rMugd/r6Xit3HI6V7c+zrDHCLkGauqbYa2Lb2OOXFEBs5vcyTmeysHnEURqxBhFxBpB0ClHzuoxUEfIRYMbd+Qen1ttaBPdiUy+WHO2HaCjlRwIvgaFXBtwduSsaGUTF28bdeQA1K2PA1qfI5fOFatGK8MBH7b1B3Gixiy524/N44bJ4dJ7Y04gTTtyNYRlyZGrcyGklNKO3Doh52/azTFiq3J3+aYrxjG/msV9p50bKhw+FUfQ58HlO5z/loN9gbbUyJnY6UDYj7//5euRLRTxa/90aEvscJ2cT5Y2DWoR8nsR8HlcrZF7ZGYZcysZPOvSUaxmC6VZj+0mkc4j6PM0tPEDaMGSzF58NUdr3YObc+Q8HsE1e4dw71RnG54cn13BnuFw2blsv+XObUb87EIig6LSHSsNPq8Hl+/ox4MuOnLV6odEBJeMRToeebVz+7G5rhqBML+SwWh0fSphPBbCK568F1+692xHN+cS6XxDwgnQ5+Zt/cFNc+SM6GjUkQM2f5ZcPJnFYDhQdwNyPBbsWLQyZY1vqtchMhraWI1cKqtHYjW/EV69F4MhEvBxILgNCrk2EE/lMFAR52nNkTPNTmofzMBapLFefZx+PA9Emhs/oJRCOl89WgnohifVHLnZRAZHzidK9XGAvnAKB7xNfyBrCTkjVubrCLmF1Syy+WJbHbnllP69/gpx/5zLxuH1SNV45X2n43jirgH4HaKi5vGWUs2fvBaTWXikvLPYgfEoPvrKa3H0fAJv/sJ9Xe3SFIsKpxaSmByt3bHS0B/yuTpHzsQq3/K8ywBsXrxyOZ1vOFYJrEX4LrZ4pakBbbbZCaDjlUcvJDoaybV3rDQcGNu8zpXTcTNupfycd9XOfjx0dtmVc8DCarZm7GzfaNRVIfWmz9+Ht/7bA649fyULVRw5AHjjT+6DCPB333u8Y+uxd2luhL3D4c0TchtIKJiRQ5tdJ+eU2nJiPBbadHfQ0GiNXDSwsRij2UBotoZNRyvrjx9IZgtdfb3SSSjk2sDyJtXINbLDful4DCLAk3YP1L2viCDo8yDdZAMWpYBgjQ/95Eik6giCOx+fBwA8ff9o2e3hgA+rTQ4Ez9RwCM2ufD1HzuzEVV7U9If8TdfIOY2jALQDdsPkkGPr5Wy+iB+fXcI1VerjzOPpznzNnbwWrF3vyjqGZ182hne84Ep88+Hz+MtbjjT12J3gfCKNbL7YkCMHtPY3bAffOzKLK3b04+o9g9jeH8KhTRJyiXTOsbaoGherkIunchBZv4GyEa6dGIRSuntsJygUFU7MrWL/WPnmxM7BPgR9nk2pkztrCTl7tBLQDU8SmTxOuxCzXkxmHTtWGvaNRXA2nmq6LKAVCkWF+dUMDk0t4mEXZ+0ZUtkCktnCuho5w87BPrz0ut34wqHTON8h130jjhyg45WnN0nImQ3YRpqddMqRW0xmG9pgGu8P4kKH/mbpBmvkohtsdmIE+ko63/Qc5fpz5PSaky6cD7oRCrk2oG1zZyHXVNfKBuZ7GPYMh/H13/lJvPBJOxt67JDf29SXYaaBPPXEaBhzKxnHAd+3H59HLOjDVTv7y26PBL1NzwNJ1RhQHvB5EAv6Sg0+qrE2Q678oqY1R86KVjqcuG+6YhuOnl9Z9yX26Mwysvkirq5SHwdoIZctFJtuVlNr1/t1z5jEK568Bx/7znH8v/vONvX4m82U6VhZZ/SAIeaiI7eSyeOeqUU8+7IxiAiumxzCPZvUVKbRDm2GkUgAw5EAjnaoTblSCl994FzJCdos4sks+kN+eBtouFCNq/cMQgQdq5M7u5hCJl9c58h5PYJLRiObIrZLm1cVQu6Ju/Rm4INnOy9WFpO52o7cWBRK1W6mtVnEk1mY69HP3jXV8eevZH5VOzajkeoNn/7nsw+gUFT4+Pc748olGpjbZmfvcBjnltNNbXTXo1QjV2cgOKC/U0N+D85t+rkp11DkezwWxHI635ENi1SjjlxQb7Y3OprECLl8UW14/Fa+UEShqEod1qthZhBvhXKQTkAh1yK5QhGr2cI696WVOXIbceQA3a2ykW5RgB5B0MxJwgwRr7V7M2nV6znFK+84Poen7BuGryI22Iojl8oWahbFDkUCdZsFnLN2v3Y61sg1KeTS1VsN33TFNgBY58odthyAeo4cgKbr5BZWq+96iwje/aKr8ORLhvG//+0B3H58rutiC+a4mhhuMFrZ554jd/uxOeSLCs++bAwAcP3EEKaX0psiZja6Gy4iuHx7DI9sUs1eJYemFvGb/3wvnvXB7+A3P3cv7pla2JRZbfFkDkNNNjoxxEJ+HNwW69hgcKeOlQbTlKbdTMdT6A/51kXPLt0Whd8rHa+TU0pZNXLV/3bNjCC47bFZvOYf7mq5yZCJ5w9HAviPw2dddfmBtWHgtZqb7R0J48VX78Tn7prCfAeieol0fkNO+N7hMJQCziy2/3y4ktF/n0Y2t0QEOwb6StcBm8VGopVAZ2bJlZqd1JkjZ75bGo1K2iOzG90MN2mxuo5cgELODoVci5iL6vWOnP5wNBWtNAdzAzVyGyXk9zTl6JjC2FrCyTglJysanpyNp3ByPomnVcQqASAa9Db9YaxVIwfoL7p6Qm5mKQWfRzBSUTjeH/K1PVoJAJOjEewfi6wTcvedjmM8FlwX8bTTqpBbTGZrztgK+Dz421dfh/FYEK/8+7tw5R9/HS/4yG148xfuw8e+cwy3PHweJ+dWXRsaPDWfhM8j2DlY/T2yEwv5XGt28r2js4gEvLhuQjus108MA9icOrlEOtfQ7rOdg9tjeOx8oiNi/aGzWhi8/IY9uO2xWfzS/70DL/7YD/Hlw2eaSixUI57KYaDJRid2rp0YwuFTix15b4xQq3TkzG2nF5Jt352fjqfKGp0Ygj4vLtsWw4NnOyvkEpk88kVVU5iYQfYbqZP78C1Hcdtjcy3XHBnh9Maf3IdktoAvH3Y3sWAcuWrRSsNvPOcAMvkiPvGDE5u6HqXUhjeTzLXCZtTJbaTZCQBs79/8WXLxVO2NCsOYNRS8EyMISuMH2ux+2dNGG722a7Q/xNqaGK0EKORaptpFu9lRaMaRM+KvUUduIzQbrTSOXC0b3jhylfGXO46b+riRdb/TiiOXrhGtBLSQq9cC91w8jW39oXVxrFjIh0y+2NSFphn+Wa34+6Yrt+GuxxfKGiocPrWIa/YO1uxq1bojl6s7omI4EsCXfuPp+LNffCJe9ZQJDEcCuPPxefz5N47gDZ8+hOf8xXdx5Tu/jp/7P7fhHf/x446KuqmFJHYP9a1zdasRC/pdGT+glML3js7iaftHS5/hK3bE0Of3boqQW0lvLFoJ6C63yWyhI/VQj84kMBT2409fchXu+MMb8Z6XXIWVTB5v/sL9eMYHvo2PfOsxzLXBNYgnG7tYqse1e4eQSOdxrAPNNY7PrmA4EnCMFe4fj6Ko1iLF7WI6nl5XH2e4aucAHjy7tCmOaTVKY1FqiPBwwIcdA6GGHbkHzy6VXFUjxJrFCKefOjiOJ+0ewGfumOro+7NuPSum+3DtWZoHxqP4uSfuwGfumNrUqF7Sit1tpOGSGUGwGXVyiQ2MHwB0ndxmCrl0To8jajRaCXRmKHipRi5Qp2ulJZoarZM7tZCE36uvY5zKbGphrpfrjh+wXMSNPv7FCoVci5jZReuild4WopXW7zgNum6VoN/bVLMT4+LVcsAiQR/GYsF10crbj89hOBLAQYfOmq3UyKVzhZqxgKFwoNTJrhrnltbPkAPWhis348otp3Pos9rfO3HTFduQLyp83+pquLiaxcn5ZM36OKA1IaeU0o5cQ18mIbz8yXvxRz9/JT7z+qfgjj+8EQ+866fxpd94Oj74S0/Ca546Ab9X8Nk7T3W0k9zU/Cr2jjQWqwSA/j6fKwPBT8yt4sxiCs8+OFa6zef14Oo9gzg01f46uY3uhgPAwe26VnWzRiLYeWQmgcu390NEEAn68JqnTuDWNz8b//i6G3Dljn586JajePr7v43f+9f7W9qJjidzLXWsNFxrxZs7MRj8+IX1jU4M5vZ2xyunl8qHgdu5alc/FpM5TG+yQ2FnYbV+VBDQrtzxBkcQfPbOtVq2Vh250tiWqB64/diFFdx1YnPqXRth3raeerz0ut1YyeRLzcY2A7NZtpFz0Fg0iJDfsymz5FbSefg80lCPAQDYMRjC+eX0pm1KbmS+pYlWdmKWXDpXgEj960yzSdjICAKlFE4vpHDpuL7W23C0coOOHEcQaCjkWmS5jiPXVLOTfBEiKO1qtJM+vwfpJhywRmeOTI6EyzpXKqVwx/F5PG3fiGMdXzig28g2QypXqBkLGI74S7up1XAaBg60NlDaaa6gnWv3DmEo7MetD+t4pZkrV6s+DmhNyC2n8yjUiS/Voj/kx7V7h/CyG/bgHT9/Jd7+gisBbH63L4NSClPzSUw02LES0GI8nSvi/7P35uFxpPd54FvV1VV9N9AAGgcJgNfwmOHcnFtzrRzbsmzLfmIdsUeyZcnnejeJ4/XGzmb9JNE+Gz9O4pVlx0diZ20psnzbkta2HB0zuubQjDScQyA5Qw4JkABIoO+ruqq6av+o/qobje6u76urQbLfv0YkAJbQ3VXf7/deqk9F3INAagcev2Vmx5+fOjCJlY2Kp7p+XTdQVdjqBwDg6GwCHAec2fB3kGvpBs5tVnZ1I/I8hyeOZfGHP34/Pv/zj+M99+3HX3/rCn7zi86LjAvtria3ODgdx2Qs7FtdRDfOb+2uHiA4NN2uIPAw8KSuaCjW1b7SSgC4zQo8CU5eSVQTw8JOgE4FgR0bVmqo+OuXr+ChQ6YCxC0jt11VwHHmYvD77lhAOhrGx58bXehJrtpEJMwjZuNtAoCHDk1BEng8fXbLt+shy06WexDHcb5VEJDwJ7vONoK5dBSabvjmJbT6LaP296apuIgQzwUjrVRMRZPd7ynBIK3cripoqC2cmDcXhU4ZOZr6ASc//0bFeJBzCfIhHVQI7pSRE0M89Y2IBZFwyJJJsoBGWgmYBeXdjNzFXB0bJXlHf1w34mLIcd9IQxnOyGXiEmRVt4bQXphl4A3Mp4Yxcs4GuVR08HYyxHN48ngWXzq7Ba2l41urBfBcJzVuENwMcgXKrTctiJfPb28BQbGuoiJr1ImVQKeQPWh55ZfPbeHgdBxLPdd67/IkWroxsBDeCaqKBsMAkpR+EIKYKGA5E8PZq/4mFK7m6zse7P1wJJvAR37gdhydTeKKw/ADraWjImtUW287cByHe5YmfU+uLNQU5GrKwEEuKoawbyLqqcRzvUjCnfoPcifmUuC5jq8xCBDVxLD6AcAcsCuyhm2bwezPX7oMWdXxz9v9jW4P6PlaE5Mx84AdFUN497378bnXNgM5bPdDrqZgKi5RnQ8i4RAePjyFL5295tv1kFAwlgoUwL8uuaqsUfvjAFjPf7+WkuT9TSP75nkO0wkxGGmlNjxjgIBFWklez1vb6eTMHjnNXvkFdNUPOCQBbjSMBzmXKFm0+c6HkJseObPZ3p+XxmlqZZOyc+TAVAxXy02L8v76+W0A/f1xABCTBNQdGlZlTbcJOzFvnIMqCEoNFbKq74rhBjqMnBNpXrmhDWXkAFNeWWqoePFSAd9aK+LYXMraMg1CMiKA45wNckSOY7f1psVs++G3XvI3tpngUp5UD9BLK8kwHmTgiay28OyFnJVW2Y17lifBccCLF70bEKoOZE0Ex+aSvksrz2yYg+KJucGDHEE2JeGqw8MxOUx6Ia0EzNfq/FYNRRuPrRtYQSfZwe/pwx4nV5LU1EGMXFQM4ZZsEq8F2JfWYeSGv3Y0gSe6buATz13CPUsTuO/AJCSBt+59TpGr7izf/pEHl6HpBv7khTVXP9fN9dDIKgmePJ7FpVwdb1HKUllRdsDIAaZPbjVf99xvWGmyDXJzVpecP8+yEln2Uy6ZsslIINLKhqLbLuaBziBHI60knsdb24s7mu/pRkdaScfIjVMrTYwHOZcoks6wnoMU0R07lVaKPiRWAi5SK2kHuWlSQWB+oL9+Poe5VAQHp/sfVuJiCEqLPVSkpRtQtOE3okmbUvBBZeBAt7SSfQiwk1YCwGNHZyCGeHz+21fx8loRdy0Ol1UC5rYuKTlLYrQYOQ+kZ4AZxDOdkAJj5KzqARZGLuqcVXWKb1zMQ1Z1PHZ0d0Jrqh1t76VPruNPYR9gjs2lcHG75msQwspmBTxnRtvbIZuUHG+iaeV5tLhnyfSrfsvHGgKremBmt3eY4MhMAuev1TxL0OwMcoOTX2/blwpUWpmvKRB4zvbwTZjLC0MGkq+d38Zb2zW8/6FlcByH6YSEbZeHYpMB67yvDk7H8egt0/jkC6uuqw2cIF9TmJQVTxzNAgC+dMYfVq7ikJFbzsRQV1quB+1e1JpsnmG/S8ELA5b9g5BNSsF45LTh9U0ELNJKwsidaEvpWYrEgS5ppc11xdrnvnFqpYnxIOcSpYaKpCTsStLjeQ5iiHcsrfSNkXOaWklRCA7s7JLTdQPPnc/h4cNTA2UgsXYfyCD54+Drsa9DIFvLQQ+KThn47kMNSZx00iVXaqgDEysJEpKABw5l8CcvrqEia7b+OIJ0LOyIJSCspFfSSsB8AAblkSOVFktMHjnnrKpTfPncFsQQjwcP9Weg712exLdWi54Z6zv+FHZG7vhcEroBvHHVv8CalY0yDk7HqSQ8s6kItqtNR7+bQaFTTnHnYhohnvNVXnl+qwZR4LFvsj87BphsXUNtYdOjnqv1kgyO6zDq/XByIY1rlSau+dytRWDWooi2UsGFiShEgR/KLH382UvIxEV8z+3zAIDphIht14xccxcD9tSDy9goyfiCT8OR7fXYJFZ2Y2kqhsMzcd/klU48cgAs6bnX8soqIyOXiYsQQ7xvS0lyb6JN1M2mJGwFINuVFTppZZxRWjmXiiAdDYPn/KsfEEI8ImHesS3nRsN4kHOJUl0dWIQpCjyaDtivptbag4Oc/eAEdG7OF3N1nLtWQa6mDPTHAR2tM+sHkjCEdqmVwGBGjsgC+zFyKRceubI8+D3Rje84MWv9/HtoB7lo2JVHzivGAiCDXDDSyq++uYVjs0mqBw+BG1bVKZ45t4X7D2asBUUvTh2YRLWp4dxVbySNRLrCWj8AmIMcAJzZ9E9Gd2azjOND/HHdyCYl6IYzTxNZbngRdgKYC6bjc0l/B7lrVRyaju+qPukGYaG8kleuFxuYTUYQHpJUd7Lt1X09IHllvqZQKQVCPIeDU/GB0sr1YgOfX7mK9963aB0EpxKSBx45Zdfg9PbjWcynIzvSMYOAYRjYrimYZpBWAmZ1wvMX8r6k/DlJrQQ6SzmvKwjMOha24JU5H5eSxboCMcRTyRgBYCYZQa6m+M72ytrw+iYCUeAhCTxVsMhqvo6lTAwcZzLsrGEkMmX9AGCWgrMMin//2gY++vk3mK7nesF4kHOJUkMdaLCXBB5Ky1khuB8dcoBJWTupH6CVVqYiYUzFRVzK1fD1N83I42GDHDnwsj5gZIrrIezToFLwzZIMnjOjkHuRcDgEtHSzHJWGGXj7CVPykowIVkKdHZwOcvn2wyROkXRGi6AYufViA9+4WMD33TnP9H0Wq9oIZmu3Xmzg3NVqX1klwb1LZjH4ix4lIjqVNQGm3zAS5nHWJ59cRVaxlm/gxNxg6WA3sinn0dusW28a3Ls8iZc9ZE97MSyxksAa5DxKrjTLwAezcUAnqODVgOSVhZpq648jODQTH9gl98nnV2EA+OH7l6w/m4qLrlIrtZaOQn13/6YQ4vHD9y/hK29s++Y964ea0oKi6czKiiePZ6G0dOuZ7CUqsooQz1GlaHZj/6Q5yHndk8jqkQP87ZIr1s0zIm14XTYpwTBgG+rjFg1KRg4A9VB2OV/H/oypMEhG2HtcaRk5wGQKWQa5T76whj969iLT9VwvGA9yLjHMD+WckfM37ETRdGbPBZFW0lzX8lQMF7fr+Pr5HJanYtYNux8sRo5R60wzyKUiYYR4bmAp+EZJRjYZ6VswHeI5xMUQ842IDH40jNz+yRju3J/GAwczfasZ+sENI5ehkC+xYH4iioqs+R4B/P+9sgEA+N47Fpi+ryOPDYaR+8ob7dqBtielHxYzUcwkJbx00RufnFNZE2C+x2/JJnHWI3awF4R1HJZY2Q1ShnvVgaSPfMZpIr5pcc/SJGpKy5dBt6m1sJqvD+yQI5hOiEhFBJynLMK2w0ZJ7hvu1I2EJODQdDwwn1y+Tu/5OjQTx2q+vqtSRNF0fOobq3j78axVNg0A00kJuVrTcaAG8Tf1Y8Dee/8iBJ7Df2dg5TZLMj71wqrj6yHs4lSf5eMwnDowibgY8kVeWW5o7SAutmdLJBzCbEryXlrpoFdzPh3BRtkfdUmxoTCl6Vql4D7LKxvq8LC4biQi9oNcU2thoyxbTKs5/LE9e2k9cgAQE0OoMpwbL2xVUWyonofr7AWMBzmXKNowco7rB3wa5IgUkbWCoKmaxliam/WB6TjOb1Xx/Fu5gWmVBISRY5ZWKvaePZ7nMBkLD/XI9fPHEZgbJbYbEWF/aL06f/jj9+M/vfcu6p9vDnLsg1O+pnoqqwS6Kwj8lVd+5pV13LE/bQXp0CIRcP3AM+e2MJeK4OiQYA+O43BqedJzRo51A03gZ3LlSrujjlZaOeuCkSs1VPCcM6/gINy7bAae+CGvvLhdh26YqZTDwHEcDmcTeNMDRs4wDKwXG9hnM8gBZp9cUNLKYl2xZPB2ODSdgKYbuw7/f//6JrarCp56cHnHn0/FRagtwzErT3pIM308adlkBN99cg5/9tJlKo/3S5fy+N6PfRX/8i9fdcx2WmXgjPdySQjhkSPTePrslvcpkbLq+HPndQWB1tLRUFvM98O5dBRXS03PQoW6UairTJJvS5ngcwUBOdPRICEJth65K4UGDKMjmY1LIccLehpGLiEJ1EouWW3hSrGBlm7ckN1z40HOJYYxclKb/WKF6ZHzKbWyPSCyJlc2VHoa/sBUHNcqTVRkDQ8dHiwzA7oTkdg+8JZHzuaaJmPikNTK4TKjZERgHgJKAwriB2EiJtoGo3QjFQ2j7GCrVKgrVh2DV5gjFQRF/zaHb23X8MrlEr6PkY0DTMYpIQmBMHJaS8dX3tjGY0enbZcd9y5P4nKh4Yh56kVV1hzJmgiOzyWxVWn6UoZ7ZrOMZETAwpBlSTemE84ZuWLdvA/TMts02D8ZxXRC8qUY3KoesJFWkq/xwiOXryloajrV63FyIYUrxcZAWbpX0HUDhbpKP8hZFQQ7GcqPP3sRy1MxPHbLztoP8p7arjl7f+fb8rZBcf/vf3AZpYaKz7yyPvTn/PELq3jf7z2Hlm4+d0l6KCtyNtczDE8ez+JKsYE3PCyYB8xlUlJy9mxZysQ99ciRc4QTaaXS0j1P0ATMHAWWWpQOI+fvINdQ6TxygCljtBuAyEBuMXKRMHP9AG0hOLkmWmnlxVwN5MjkRNG01zEe5FzAMAyU6irSA+Q8osA76pFTWv4xcmQYYw08kRk+9N0R8Q8NSO8jIAdQpx65qDj89zQZF/seRswycBlzqcHbaTeDnBPPEg3S0TCUls48iOdr9FtvWpAuKj8rCD572jwgvfMONn8cQcrBa+gEpy8DLL0MAAAgAElEQVQXUZG1obJKglMH2j45D/rkKrKKhMQuayI43u5380M+uLJRwYm5FPW1iQKPqbjo6ABTYGB1aMFxHB48lMFX39z2nMUgnrdDNtJKwCxMv1Zpul5IkIWLnbQSAG63Ak/8lVdWZA0t3aBWCxwiFQRdg+3KRhnfuFjAUw8s7xrkreRih36jbRsG7P6DGRydTQwMPVE0Hf/HX7+KX/rLV/Hw4Wn81c8+AsD58suptBIAnjhmDrle1xBUHEgZCZYyMWyWZc8qUCptKR9r+JOfXXKs9yayfPBbWimrraFhcd1IUgxyaz2DXFISUGW8Z7ENciHUKNPOuxc/xE99I2E8yLmArOpQWvoQRm5v1g8ATgY5ej01qSA4NpvETHL4AyfukpGzYy4zMbGvR64sa6grrb6JlQTJSJj58ES+nrb8kxXkvca6VWLtHqJBNmW+tn4GnnzmlXXcfyAzsMDYDslIOJBC8GfOboHngLcdGc5AA8BtCylEwrwnfXIVmd3Y341jVnKlt4Ocrhs4u1nB8Xm6oBOCmaTkKPa+1FB9+cw9cSyLrUoT397wVmZ4fquKfRPRgemm3bD601z65K60WSAqaeWCOci9dsVfeWWnFoXutUtHw5hOiDt+F5947hIkgce7T+3f9fUWI+eQcc7bDE4cx+GpB5fxyuUSTq/t7Bzcrjbx1O8/j088t4qfevwQ/uDH7sPyVAySwDseGJxKKwFgPh3F8bmk5z452pTmfliaisIwgMsFbwYoMmwkGe+JxKvqdRWLYRhD7Tf9IAo8Mg4XWixgUVnReORW83VIAm+d+ZykVjZVM7GdZvnHklrZHRY1ZuTG2IFig0ReDxjkwryLQnC/Bjnn0kra4ZJ4mYalVRK4Z+RsBrlEf0ZuWIccQRDSSlY4GeS0lo5Sg16+RAtJCGE6IflWQXB2s4JzV6vMaZXdcPIaOsEz57Zw99Ik1TARDvG4c/+EJ5K9CmP5bS9mkhKm4qLnjNyVYgPVpmYxfrTIpiKOGTkW+RItSALp02e3PP2557dqVGwc0Dlkuk2uJJ9TmqVIOhbGYiaK13xm5Mi9meXedGg6gQvb5u+iLKv4q29dwfffudDXh9Rh5JwdinM1BTyHoe+tH7x7H2JiaAcr99qVEr7/Y1/F6bUiPvq+u/BL7ziBEM+B4zgsTERdMHIK4mKIqYalG08ez+LFiwVP5eZuGTnAuwoC4uOKMw5yB6cTiIZDnie1NlQzZZR1yZRNSr565AzDYFrO03jkuqsHACJ9ZMxiYCAxWKSVF7bHjNwYA2B3aHdTCC4O6flxAynsLOyEhYZPR8P47R+5Bz/7xGHbr7XCThyaYu3kniYjp+4yMW8M6ZAjcBJ20pFW7p1Brtj+Wq8ZOcDfCoLPnF4HzwHvuN35IJeKsrOqrMjXFLxypbTLnzMM9y5P4vX1sutep4psXz5vBzPwxFvmZaXNYLEycrMODzBFBp8VC7LJCG5bSOGZc94NcoZhUFUPECxmYgiHONc+ufViA5LAU1c0nFxI43WfkyuJf5nl3tRdQfBX37yCutLC+x9a7vu1pJ/OaZR7rq1kGOa9TEbC+MG79+HTp9dRrCv4m5ev4B//9tcBAH/xMw/jXXft2/H1CxMRq8OUFflaExkH/jiCJ49loekGvvbGtuOf0Yuyi3sQSRj1KvDEaa9miOdw60LKcylxpxaF7TWbSfpbCt5k6GsD6Ni1tXxjR2IsYfFYAmSaGj1LSKSVNLL3C1tVHGkHSxEC5kbCeJBzAfIhHbStcx52olPFrzpBRHAmrWyquvW9NHjH7fNW+tIwhHgOkTDPfKAlKWG2YSdx0ep26wYNI5eKCigzsjnlhgrBRfiEHZwMcn6UgRPM+VQKbhgGPn16HY8cmbbkUU4QBCP3lTe2YBjA48foB7lTBybR0g2cXnN3cHCzDSc4NpfEuatVTxPbzmxWwHGmvJoF2ZSErWqTubutVPdHWgmY3qKXLnnHYmyWZdSVlm1iJUE4xGN5Ku7BICdj30SU2rN4cl8aF3N1XxchRPbOctA9OB1HrqagWFfw8ecu4c79adyxf6Lv1wohvp1c7JCRqzaphsynHlxGU9PxgT94Af/0Uy/jzv0T+PT/8jarXL0b8+koNpwycn3KyVlwz9IEkhHBM3ml3k4BdHoPmklIiIZDng1yhDVilVYCZsDP6+tlT++DnVoUVkbOmTKBFrTnJ4KEJKCp6QPPs4ZhYK3NyBGQ14Alkbyp0p99Y6KAlm7YkiWGYeDCVg33LJn3iDEjN8YOWOzLoEEu7DDsRNMhhnxKrWx/SFj77RoMUbWsiIsCe/2ASjZKNoxc23uR7/HJbZRkcFwn8rwfUpEwFE1neg1LDdMv4GVfWzecDHJ5F74KOyz4xMi9crmE1XzdUVplN1IOWFVWPHNuC5OxsBUQQYN7lsxo+5dc+uQqssa8fe7FibkUGmrL0xjwM5tlLGdizBKn2VQELd1gSktUWzoqTc0XRg4wewFbHrIYpErArkOuG4dn4q4rCNZLDczblIF347Z2MfjrPvrkrEGOiZEzB+BPvrCKN69V8f6HDgz9+umEhO2Ksy18nnJwOjGfwn0HJvHK5RKeenAJn/jwAwMXUAvpCK5V5F1deDTYrip9O+1oIYR4PHZ0xrMagpqiwTCc135wHOdpBUHVISMHmIuLutLCWznvCt5LZNnPeG/KpiRsVfypQwA6iiwWjxyAgVLGYl1FpantYuQAMPnkZIbE9k7i+fCfv1VtotLUcGI+BUngxx65MXaCfEi9llY2tZZvjByRRzacpFb6xDLFpBDqjsNOhv+eSP9Pvmcju1mSMZOQEB4iYU066CEbVkfhBRwxcg623rSYS/tTCv6Z0+sIhzh8121zrn5OMmKyqn6VgOq6gS+f28bbbplBiCH6fiIm4pZswnWfnJttOIEfgSdnNirM/jjAWSk4+SywBAqwgLAYXvnkiNftCKW0EjADTy7ldhdhs2C92MBCmj406GQAyZX5mgoxxCPO8Gwh3sL//KXzmIiF8b02ibZTCdEFI6dQSxn/w7vvxH/74H34yA/cPtTjPj8RhW44q9nI1+gYwmF48lgW1zwK8CGKFTfy7sVMzHOPnJMAKPJ+f81DOXHR4b0pm5Sg6UbfoDYvwMrIkYXcoOd8b/VA9/fQ+tiAtvKL8uxLG5RHZNiHZhKYiIWtc/uNhPEg5wJ2BwgnYSe6bkBtGb555JxKK2WtxSStZIETRo6UWdr1RhGPRL6288O7XmoM9ccBzga5sqw5TvCiQTLihJHzzyNHevi8LAXXdQOffWUDjx/NupbLpaJhtHSDeXFBi5XNMrarTTx+lF5WSXDqwCS+eangeOtqGEa7jNfd7+jobBIcB898cnVFw1u5GrM/DuiU4W4xyIqK7cOOXwsUIcTj0Vum8cw5b1iM81s1JCOCbaJvN45k+xdh00LRdFyrNJnSX6cTEubTEU8Ptr0o1BRMxtkUDEuZGASeQ7Wp4T2nFm1ZhamE5Lh+IFdTME1531yeiuPJY/b1I/NW1D3bIGcYJlPtpHqgG+Re5cVigqgd3NyDCCPnxWeLeOTiFGmwvTiSTUAUeE/f706XqNlkuxTcJ3mlrLJ55JIOBjnyPSznJzPshHK4bC9/7M6O1iA3HcdEVBx75MbYiWJDsUqH+0ESQsyMnNLeuPrmkbPqBxillYpuBaV4jZgYQp2yD8S6Hspeu8m2tLK3FHyzJA/1xwGwSk5ZpHmlhupbhxxgegqTEYEpUp+wkX4wFqQU3Et55YuXCtgsy67SKgnIMF5u+OOTIyEYj91iXzvQi3uXMyjLmuOC3qamQ20ZruoHAJOlX87EPEuuPHe1CsNAYIyc00ABFjx+dAabZRlnr7r/HZGgE5bhhQSjOE2uvFqWYRidxQstbltI47V1/6SVeQf9f+EQ307HA37kgSXbr5+Oi47qB9R22q/bwakXpP6BtRS8LGtQW4ZrifxMUsId+9Oe9MmRQ7obVcBSJoq60nIcSNONaruOxW7B2w/hEI8T8ylPKzesHAVWRi7lbyk4WWyySivtBrnFTJT6e/pBZkhHp2X8LmxVIQk89k1EkY6Fxx65MXaCyOgGPZCdFIKTwc83Rs6qH2ANO6EvBGcFS4wsQUOhSzciLFSvR26zJGPeRmbkiJHzWVoJmMwDKyPnJrJ6GMjv0Kl5vx8+ffoKImEe33Fi1vXPIpIfv3xyz5zdwon5FFWwTy9OLZs+Oad9chVL1uR+cXB8LuXZIHemLdk64YCRIywVywGm4PCwxAJS9O4Fi8GSWElA5ITnHXbJkaGBtY/x5L4Uzm9VXaerDkLBYb/lP7ptFu89tYjlKXuf4XRCQlnWmNUxThI1aUAK2VmXX50ycPfX88SxLL65WrDYbKfoMHIuBrkp75Irq03V1WLr5EIKr62XPJPiF+sKImGe+dlLFlpOOjVp0KRM/Sawk1au5euYTog7ejEJK2pXW7DjupjqBwgjZyOt3K7h4HQcPM9hgvHsdL1gPMi5QLE+/NAuCTzUlsEknVIYmu2dIOK0fkDzL+wkJoYcFYLT3IRiooBImN8RnlCRTWOuLSPnYAjYi4Ncoa74klgJALNpb0vBtZaOv311E28/McsclNEPFiPnwyBXbWp46VLBkawSAJanYpiKi3jpojOfnBeyJoJjc0lczNWYFzz9cGazgrgYwuJkzP6LeyAJIUzGwrjGEL1d9NEDSjCXjuD4XBLPuBzkKrKKq+UmDmfpg04A8zWeTUmOkyvXGTrkunFyIQ3D6NRJeA2n96ZfescJ/Pt/fAfV1xJGjdUnRxgiN+Ei/ZCQBCQjAjYYGblOGbh7hvDJYzPQDeDLLgN8rGWSi2feUsb8LHjhk6s23YU/ndyXRkXWPAtfKdZVTETZ3z9OFlosYGXkLGnlgKFsrVDfEXQCdJ69LIwcW/0APSNHFmcTY0ZujF7YBVsQw7PCYFAnDB6tTpgVZEBkkVZqLVPC5QejA7QZOeZCcPoyy0xsZyk4kW3ReuRoZXmGYViplX6CnZFztvWmgVkKLmKz7I1H7uvnc8jXFNdplQRkyGGtkaDB197chqYbjgc5juNw7/Kk48ATL2RNBMfnktAN4I2r7pIRAfPQf2wu6UjeBJj+kKsMXXJWn6ePjBxgshgvXsq7CvYhfg1WRo58j9PkSlJAzRJ2AnQCIF697I9PrlBXLR+zX+iUgrOxT2Twy3gwOPViIR3FFUYVA7l+L+7ld+yfwGQsjKddyiuJxN/NPWj/pPme9GJ4qrSllU5xcoEEnnizuCjUVUdKgZgoICEJTF5hFpBBjjbAjkZaudQzyCVsWLx+kFUGRk60H+QUTcdaoWEpGtLR8NgjN8ZO2LEvZBhjifonjNyw1Cs34DgOksBb1DoN5PY1+SatFAVmj5zMUIcwGRd3eOQIe2QnrUxZQwDd0FRXWtB0Y28ycj4elubTUeug6BafOb2OpCTgCYZOtmFIR9nlsbT4f792ETNJCfe2JZJOcOrAJFbzdSYGisCK2vaAuSTJlSsuA08Mw8CZzQqOz7P74wiyKYlRWml6lZ10R7Hg8aMzUFsGvvamcxajUz3gbJA7v1V1JPtaLzYwGQszJw/PpiRMJ0R84cw1z5NfW7qBYl2hLih3CsKosfrkrNoWjxk5AJifYO/fJIOlm15NghDP4fGjM3j63JariHsvUisj4RDmUhFcynnDyLkZKo/OJRAOcXjNo6TWUkNxLPnOJiVHzwUaWGEntMEiQ9gvtaVjvSjvGuTiNixePzQZ6gdoGLnVfA0t3bAGuYmYCFnVPVGe7CWMBzkXKDaGb1vIZqHZon/TNH2WVgLmjZPljSxbNLxP0kopxO6RY6hDyMTFHR454ueyY+QSjB45MvDttUHO7ELyV3a26YG0sqm18Pevb+I7b5vzjP21GDmPdfEvvJXHsxdy+KnHDrlauty7nAEAfNMBK+eltHJ5Ko5ImHftk9soySg1VJyYY/fHEWSTESZviClf8q+7keDUgUkkJMEKuHGC81tVCDyH5Sl22enhmTgqsoYtB8Ed68UGs6wSMBd/P/34YXzljW383pcvMH//MJQbKnSDrUPOCcjgw8rIEWmlL/2bE1FmOXreQ0YOAJ48nkW+puAVFymNFVlDOMS5Pq8seVRBUHXJyElCCEdnk54lVxYcSisBU155jUGZwAJLWimysV/9zkIbRRkt3dglrRQFHqLAM0or6esHYqK9R+68lVhpLs7I2czr88CoMR7kXIBWWrmXGDnAZNZY4thJ54hfqZVxUUBT06ExSFAbCn34Sia+U1pJHqAkGWoQSCIp7SBnFcR7cLAeBmZGruafRw4wB+J1D+oHnjm7hYqseZJWSdAJO/GWkfvYF9/AdELEjzyw7OrnnNyXgijweNGBT67sobQyxHM4Opt0PciRCgM3jNwsYxlusa76LqsEzFS7R45M4RkXZcrnt6pYnooN7a8chCNZczg+f4098GSDItxpED70toN45+3z+NW/P4Ovu2Aje0GWa37JvgmIR46dkWtC4Dlf7ucL6QjyNYVpoZqrKUhGBM/OBo/dMgOOg6v0SlJ/4naJsuhRKXi16W6QA0x55WtXvAk8KdZVKzmbFdlUxDePXJPRIxfiOcTFUN+hrF/1AEFSEthTKymvSRJ4CDw3lAQgnuIOI2e+FsXxIDcGYHZdlRrmJngQJAceOat+wCePHGAyayweOeLb80taSTYrdSa5J70pdrLHI7dZbmA6IVL9jpMRgTrsxK4g3iukomEoGp08QFZbqCktXw9L8x6Vgn/mlQ1MxsJ45Ah7lP8gRMLmzd7LsJOXLhXwlTe28ROPHmKWqvVCEkK4c3/akU/OS48cABybTbouBV/ZML//mCtGzizD7U2aHYRiw1/pcDceP5rFlWLDsVft/FbNkawSgBWQ4iTw5EqxgX2M1QMEHMfhV3/oDhyaSeDn/vhbzLH5g0Dk7n6/dnExBEngrbAQWuSq5gLMqddzGKy0XwZWbrva9ERWSTAZF3H34gSePutmkNM8Sc1dysSwWZZdS96qsruwEwA4uT+NQl3FukuViemZV5B2yMgRaaXXkmaAvRAcGJwuPmyQS0ToBznDMJhSKzmOs008v7BVw0xSslQrhB290QJPxoOcQ1SaGgxjeFqTE48c+Vo/GTl2aSUpj/Qv7AQA6gzJlTJl/QBgbnwrsga1PSRvUHTIEZiDHK200vy6IKSVAF0puNNCUhYQiaobeWVd0fD5b1/FO26fd8RWDALHcUhFw57WD/zGF95AJi7iqQfdsXEE9yxP4vX1EvMhhngPvPDIAebwtV1tOurcIjizWcH+yagrFmO2XeVAKysq1IYv1LwE8W46qSFQWzou5Wo4nHU2yM2lIoiJIeZBriKrqMiaFXvvBAlJwO++/14omo6f+cRLnnhMSG2E34wcx3GYTkjM7+ucj5L0+fZQzTIU+xFa9eSxLE5fLjkO1Si3GTm3IFLjywXnSwJdN1BVNNde2ZMLpprAbcBPTWlBbRmOPaDZpARZ1a2Scy8hay0IPMf0rE1EhL7XspqvIxzirPv2ju+RBGqPnNoyYBhs58y4GBoqrbywVcWh6U5CsMXIuazd2GsYD3IOUbK6iwbfWC2PHEPUv9L20/k5yEnhkBVgQoOG3x45S+tMf8OirR8AOh4MMtRslmTMpegONclIGJUmJSNHpJVRf0MXWAa5vNWF5N9BlwxyrOb9bnxh5RoaasuztMpumAXq3jwMX14r4plzW/jwowc9qUcAgFPLGagtA6fXikzfV5FVxMQQBI8GX1Lg7UZeeWaj7KgIvBtE8nyV0uhfaqhD78NeYmEiiqOzCUc+ubV8HWrLcMzIcRzXDjxhk1YS1seJR64bh2cS+I/vuROnL5fwbz7zuqufBXQxcj4PcoAZeMKcWllt+hJ0AnTSQ1kGuVzV+8HyyeNmP+KXHfo+K7K7cBEC4q9azTvrSQRMRY9hwDUjd2I+hRDP4XWXgSdkWHAcdkJKwX3wyTUU+tRvguSAoWytUMf+yRhCfZjrOIO0UrYS2+mfZ7aM3HYNh7rut+TsNJZWjgGgK/KaRlrJMDQRRs7XsBOBdxR24mdqJcDGyLGEnZCHHxlqNkoyFihlRiyMHM17wgswMXI182v8Tq0E3HXJfeb0OmZTEu4/mPHqsiywyGPt8BtfeAMTsTA+8NABT34eACv1klVe6TZquxdEDulUXimrLVzYrjkqAu9GNml+NrcoDzDFuvNkOCd4/OgMXngrzxzQdN6qHmDrkOvG4Zk4zjPKOq+0hwWn0spufNdtc/jZJw7jj19Yw598Y9XVz8pbagH/X7spB4ycGRLlffUAAEsRwnLPzNUUy+/nFW6dT2EmKeFLDuWVpkfOG2klAKy6SK7sKBTcvZ8i4RCOzCRcB54UKZb9w0Dug34kVzZUekUTQSLSf2hay+/ukCNg8cg5OfvGJGEgI5evKSjW1R33W+KlLo2llWMAsLoohqZWhgkjx+6R81tayVQ/4LO0MiaxMXKGYTD1yJEhJl9TUFc0lBoqg7QyTC+tbHiXIjgM1iBHcTMKIlDAKgV3WEFQaqh4+uwW3nn7Qt+tnlukGF7DYXj1cglfPHMNH37bQU8HqExcxPJUjHkD7DZquxczSTNq/qzDCoI3r1XR0g3XjFynDNf+/aRoOmpKKzBpJWD2ySktHc+ezzF9H/HVHXLIyAEmK3al2ECdQb1AWB+nYSe9+BffeQyP3jKNf/03rzOzyN0o1BRIAu/bgrAbU3EnjJx//ZuRsNm/Sati0HUD+VrTc0aO5zk8cXQGXz63xRQ2RmAycu4/e9MJEdFwCKt556qOals545aRA8z+xFevlF3506xBzuG9iZxRfv5PTuMX//w0/ublK65k791oMtQ3EcTF/kOZ2SHX/97C4pGzOpQZ7geJIYnnF3qCTgBzsAzxHFNY3PWA8SDnEDTsixhqe+T2GiPHGHbit7TSYuQoDyfk90l7PeRhXKipXR1yLIwcvbSS3Cj8BBsj5798yW0p+D+8vgmlpXuaVtmNZETwJOzko194A6mIgB99+ID7i+rB8lScObXNK39KN47NOQ88WdkgiZXuGLlIOIR0NExVCm4t1AKQ5xGcOjCJmBhillee36piJim5YuyJv+4Cg7xyoygjxHPIJr1hc0I8h4++727MJCT8zCdeQs7h4ZJ4vvyujQBMRi5Xa1IfzJtaC5WmZnXQ+QGW/s1iu6rBD6nnk8ezKMsaTjvwhJlhJ+7vQRzHYcllcqUV/uTBku3kvhS2q01XqZEFS1rp7DU7NB3Hr/3QHbh7aQKfe/0q/umnXsapj3we3/3/fBkf+ey38fTZa0wLnW6wWFMIEn3USaWGimJd7Rt0ArB55GQnjJw4WFp5wVJAdBZnHMfdkKXgnpzMOY77bo7jznIc9ybHcf+yz99LHMf9Sfvvn+c47oAX/+4oUaRIKCSMHJO0MiBGTmbw7cmMUbWsiLcZuSqltJI1cYnE/+brihXIQe+Ro/dXlWV1aPiNV2D1yHGc860gLebSEcfSys++soH9k1HctTjh8VWZ8IKRe+1KCZ9fuYoPve2QL4zrciaGS7k60wbYK39KN47NpnDuagUtByXBZzYrkAQeB6acSwcJZlN0Zbhut95OIAkhPHx4Gk+fYyvJPr9VxREXbBwAHGkPciyBJ+vFBuZSEc+8lIC5HPvd99+L7ZqC//VT33LE5hTqwaWNTidEqC3DCqSyQ8db7I+0EmjXtlB65PLtMnA/GMJb21UhF7fZ/Gkt3fBUFbA05a5LjjA/XjFyAFzJK4kPy6l0mOM4vPvUIn77qXvxzX/9j/Dpn3sEv/jdx5CJi/ijZy/hx/7bN3Dnv/kHvPd3n2WuBZEdSCv7ySTXhiRWAu1BjpWRY0hsT0jCQCXX+e0qxBCP/ZM7r20iGh6nVvaC47gQgN8C8A4AtwL4JxzH3drzZR8CUDAM4wiAXwfwq27/3VGDjpFzEHai+V8/EA2HrGGIBv4PcsQjx2aKpR7kiLSyqjAzcqlIGEqLLuq/bNMr6BVSjKmV6WjY00NcP8yno46klYZh4JuXCnji2Ixvm/lkJOy6APRjX3wDyYiAH3vkgDcX1YPlqRgqssYk+fDKn9KN43NJyKruaDN+ZrOMY3NJTxjpbDJCx8jV/feA9sPjx2awlm/gAuXh1zAMnL9WtSoEnGJ5KgaeA1PgyZVig/p+x4KT+9L4yA+cxNfezOE//MM55u/3I4VxEKYZu+SIDNOvsBOArRSclJN7WT9AMOcwrKrqcf0JYeScyhm9TPG9dT4FjgNeu+JMZg4AxfYywIuOyxDP4Y79E/jZJ47gkz/xIE7/ynfi4x+6Hz/+toP49noZf/TsJaaf54SRI8Ei3a8PGeQGeeQSktkRTENmsCqtzGsKoTaAALiwVcPy1O4QlnSMrYf3eoAXp7v7AbxpGMYFwzAUAJ8C8K6er3kXgD9s//efA3g7F4SewkeUGiokgR863DjxyDUdJPewgr1+wN9BLtaWVg6Lke2GxchRhp2EQzxSEQGFuoLN9sOKpX4AoCuULjVU3xMrAfOmnpQEqptRrqYgE8Ahdz4dcZRaebnQQKWp4YSLAmk7pKKmIdoJywSYksHPvX4VH3zkoG+DOnkQXmIw+1ebGpIujf29ILJIVp+cYRhY2ajghEt/HEG2XQpuB7fJcE7xxFGzhuAZyhqC7aqCsqw5TqwkkIQQljIxJkbODHfyxh/Xi/ecWsQPP7CE33nmPP7u1Q2m7zXLkoMZ5MhARuuTI51zftUPAMDCRATVpkYl+yYMoR+DZSQcQiYuMisqyHV7VZi+lImhobaw5VCqS6LxvRjk4pKAQ9NxvOqSkYuJIV+W8lExhEdvmcEvveMETu5LM3vnZFVHhLEDNRERoOnGjvPsqt0g1z4/0QRDkXMmy+8rPlRaWd3hjyMYM3L9sQ/AWucGiMAAACAASURBVNf/vtz+s75fYxiGBqAEYMqDf3tkKNVV28MDeUOySCvJ14o+MihSmGeqH7DCTnwaLq1CcEpGruHgA5+Jm6XgGyUZk7Ew9VBKHlI0PrlyQwuEkQNMVo6GZSrUlEAOS3PpCMqyxpzkR3xVfg5yRApJq9XvxW9+8U0kJAE/7hMbB3R6lFiYMD+klbdkk+A49uTKrWoT+Zri2h9HkE1GqMpwO8lwwQ5yi5kYDs/E8TSFT05r6fj1z5uMlZuidIIj2SReXi1SLSZ03cBGqeHbIAcAv/J9t+LOxQn8q79+DTrDsiRfVwJJrARgpU/S+vmIlNHrlMhuWGm/FEoGct1+MZhzqQhzD2jFB0YOgGN5pdcM4cl9aVcVBMV6MP2W00n2RFZZbTGf54j3sHupvVaoYyIWHjjMk6GaRl5JBkSJiZEzGb9eabfWMlUl/YKlxh65/ujHrPXezWm+BhzH/STHcS9yHPfi1pazXpOgUGwotod20UGPXFPTEQ5x4H0MzIgIISiaTv3QbagthEOcb/K8cIiHKPDUjJxVh8CwUcrExTYjJzOlt7EyckENcukonTwgXwvGh7LgsIJgZaMCjjMlfX6BvIZOAk/OXa3gb1/bwI89fMDXrrLFSbZBTmvpqCstT/wg3YiKIRyYiuPMBtsgR77ebWIlwWxKgtoyrNLoQeikBwcrrQSAx49m8dyF3FCZeq2p4Sf+6EV88vlV/ORjh/DQIff7yx+8ex+uFBv4/MpV26/drjWhtgzquhUnkIQQfuSBJeRrCrXUVGvpKDXU4DxySfPf2a5RMnJV/9N+yWuyTqFkINJKv9QVCxMRrDtl5Dx65nW65BwOcu1hwat+z9v3pbFRkh0nRZq1KMF0JG4zJrKy1DcRkN9r97J2Nd8Y6I8DGAc5izCgv65OB/HOe/BaoQG1ZewoAyeYiInj+oE+uAxgset/7wewPuhrOI4TAKQB5Ht/kGEYv2cYxinDME7NzMx4cGn+odRQMREd/iG1CsEZEiIVTfeVjQM6Eklayae5vfE3IjouhqgTmAhDyKLxzrTjp9dLMpNfJGkxcpTSSp+rBwhoB7lCXfG1DJyASFVZt7orG2UcmIpb8lo/QF4TJ4Pcx774JmLhED70toNeX9YOxCUB0wkJl3J0B2HiC/AjeOXYbBJnr7INclZipUcDOelQuloe/n4q1FUIPIc446HECzxxbAaKpuO5C/1rCDZLMt79O8/iy29s4yM/cBK//D0nPPGBftdts9g3EcXvf/Ut268lqYgLHlUPDAIJKnqZso6g1FBhGP4OSt0gA9A2ZQphrqYgHOKQ8nhR0o15hlLwfM3sSvRrmTqXjli2A1p4zcjtn4yC44DVnLP042pTQyTMI+zR7+i2BXeBJ8WGvWrLC0wnJFSbGrNdhvVM128oG9YhB3SklXSMHKkfoH/9En2GS6C7eqA/I1eWNcdWi70IL97x3wBwC8dxBzmOEwG8D8Cne77m0wB+tP3fPwTgi4abgo49gFJDs91ECTwHnut0w9GgqbWYejScgJhJaT/4TvTUrDBjZNk8ciym2MmYaHnkaP1xQDcjN3wIUDQdDbW1pxg5wzBQqAXjQyEHRZrtcjdWNsuuC6TtQA5jtOmjBG9eq+Czr6zjAw8fCOR3uDxFH79NhlKvpZWAKf+7mKsxBSKd2axgLhXx7Pc0myJdcsMP3sW6iolYMBH2vbj/YAaRMN+3huDb62X84H/+Gi7lavivP3oKTz247Nm/K4R4fPCRA3jhrTxetYmMJ0OCn9JKwIz4TkgCXl6jK7Un0exBeeSEEI/JWBi5Gm3YSdP3aoRsUkKI5+iklT50yHVjPh1Foa4yDQMV6x7kzTMvEg5hLhXBpTxbembnejTXZeDduHXBVBe8vu4s8CSoVNaZtvyXxlNM0FDYGblEjzqppRu4XKjTMXIUi3CnheDA7uoq4iE+3M8j1x6u3Qag7SW4HuTanrefA/A5ACsA/tQwjNc5jvu3HMd9f/vLfh/AFMdxbwL4eQC7KgquN5Tqiu22heM4iALPVggeICNHW0EgOyiPZEVcomfkiEeOlZHbqjRRqKuMjBydtJIcrL1IqKIBzSBXU1pQWrqvBwCCbPvgzcLI1ZoaLuXqnsnxBoEsXGj7AAl+84tvIiKE8GGf2TiCpUwMq5RhJ+T96AdjcGI+CcMA3rhGz8qtbJQ988cBHUbumg0jV6S4D/uFSDiEhw5N4emz13b8+dNnr+Hdv/N1GAbwZz/9MJ48lvX8337PfYuIiyH8/lcvDP26ziDnn7QSIKl6aZxeo2Mv8jXzsxhEEBPBVEKiDjvJ1xTLV+cXhBCP2aREtfzKVRWf/XokuZL+/u01IweY8krHHjkPqxAA8xm7PBVzzMiV6mog5wFLNswgAZU1nYn5AnazX5tlGWrLGDrIWecnBkaOJVQvMaC66sJWDZm42FfaSp4XxfEgtxOGYfytYRhHDcM4bBjG/9X+s//TMIxPt/9bNgzj3YZhHDEM437DMIY/fa4D0PqhpLYfjRaKgw8YKzqM3N6RVsZEgT610kGKZiYuQmtT6XNMHjk6WR4ZqgKTVlJE6Fpl4AEcliLhEKbiIlNyJQnU8DPoBOj2yNEzche2qvj06XV84KFlXw9Q3VjKxLBRlqk8tWQo9XIDTXCsPVjT+uQUTcf5raqnr2OWgZELKjCjH544lsXFXN3q4Prk86v40B++iOWpOP76f37E2up7jVQkjPfet4TPvrIxdHmyXpQRE0OBKAXuWpzAykaZitXpMHLBvXbTCZF6kNuuKr5WDxDMT9DVtuRqiq8LOScVBBUfVAFuSsGrsupJYmU3Tu5L4zUHgSeGYZjSyiDCTqxqDbr3dks3oGg6eyF4j7SSLB0XJwcPcv18dYNghZ0wFoL3+/kXtmp9/XEALEsUSTy+EeDvxHCDQm3pqCktqg+pJPDMYSd+M3LkA0wrnZIdGGNZEZdC1KmVTQdhJ90SHhZGjty87IaAMkWvoJdIR8NoasP77XI1/w373ZifYCsF7yRW+i2tZGfk/stXLkAUeHz40UN+XdYuLGViMAyzksEO5GHqh7RyKRNDJMxTJ1de2K5CbRmeBtZEwiGkIoI9I9dQkbbxKvuJJ46ZXu4vnb2G//vvVvDLf/UqHrtlGn/60w8xSbid4IOPHIBuGPjDZy8O/Jr1dodcENLTuxYnoOkGVdJfIeB7E2AycrSsRd7nwYlgPh2hZOSa/nbaMSRoEpRlDZLAexqvv5SJ4Wq5ySTxJKg2Ne8HuYU01vIN5kN/pWl6sIJYorJ2JDYZe3gJEj3s2lpheBk4wCatdFI/MNAjt10dWPVCFDpjRu4mh1UGTrEJFgWePezExw45AJYHj1Za2bgRGLmYs0EuxHNISILtEGAxcgH0yJn/jr3O22LkAjoszaXYSsFXNspIRQTs89m/06vtp8HzF/J47JYZzCSDYeOArgoCCnmlH7ImghDP4ehsEmev0nlDCHPnNbOaTdmXgo9SWgkAy1NxHJiK4d//3Rn87jMX8NSDS/gvHzjl+YGyHxYzMXznrXP45POrA2XpflcPdIMEnnxr1T7wJF8PTi1AMB0XGQrBm8j4LK0EOqXgwyIDtJaOYkP19XqssCqbxUk3KrLqedgSGQouF9hZuYqseZ7ie3KfM59csRac1YIM+LRBPp2MAWeMHBma1vJ1hHgO80Nk23GRRVqpg+eAcIh+6WQxfl33v1JDxXZV6dshB4w9cmO0QbqL6KSVPJpMYSe6r2XgQCfelSXsxG+5J0tqZUNh77XrHmZYN+XJiGA7BJRGwMh1/7v9QEpkg/KhLEywlYKbvqqU72xBOMQjGg5R37jrioa3cjXfJZ+9WGLokrOklT6l6h2bTeIsJSO3slGGGOJxcICUxSlmUxKuVew8cqOVVgLAd5yYhdLS8a++5wT+3btO+pYs2A8ffvQgSg0Vf/HNK33//kpR9n1RQpBNRbCQjlAlVxZqCqLhEPNh0g2mEhLKsmZrdZDVFmpKKxBp5UI6AkXTLfVEPxTqZsLntI/XEwmHMBkLM92/y7LmuUeXJCBeovQKd6Pa1KyuM69w0mFyJalFCWJRIQmmeoF2SUE6hFkZuWg4BJ7rsGur+ToWJiJDU0L59iKcKuxE0yEJIabzAEkr7g7KG5ZYCcBS0t1IpeDjQc4BWA7tkhDac4wc8cjRXpestpg/9KyISQJ1mXRDbUEM8UwHJiKTSUfDzFH3qUjYlpEj0kuvOnXsQDPIBZ0Mx1IKrusGzm5WcMLH/rhupKL2wzjBuatVGIb/3r1ezCQkRMMhqkMM2XD65ck8Pp/CdlWhSkJb2azgSDbhWew3QTY5nJGT1RYaamskHXLd+IXvOob/8c8fx088dijw9Mx7lydx5/40/uCrb+3qBW1qLWxXm0y9mW5x19IETl+mYORqaqCySqAjQcvbdMmRoSoQaeWEvaQxb12PvwzhfJpNUVGRvQ0XAbpUCQ58ctWm94zcZFzEvokoXmUd5NpDQlBqgemkhC3KQY4wcqzLeY5rD2XNziA3TFZJEJdCVGcCWW0xX1M/D96FLdOvPIiRS48HuTEAoNTettAMciKzR67lqea8H6zUSmpGruX75jQh0dcPOEnRJMMMi6ySgIaRKwcddkLJyIV4f7uQusGSfLZWqKOmtAIblpKRMHWPHPHu3RrwIMdxHLXZvyJrCIc439h74nejYeXOeJxYSZBNSdiqNAfKzsh7f5TSSsC8nx7J9t/++g2O4/DjbzuIt7Zr+FJPeiYJQfE7sbIbdy1OYC3fQM7mUFmoK4EGnQBdEjSba8u3QyOCCDmiqW0hv0u/B9/5NJvHuSKrni8up+IiYmKIeZAzDANV2XuPHGDKK1mlldYSNahBLiFhu0Ln45MdpH4TdA9ya5SDXPf3DENTZVejkf8P3bacC9tVCDw38NqEEI+kJFis6Y2A8SDnAJ0DhP2NVRJ4ptTKZiCMHGv9gO57/UBMDKGhtqhKGp0MlqmIgBDPOQogoJVWSgIfmFSIlpGbDLBji2z+aSoIOkEnwQxLKYrXkGBlo4yEJGD/ZHBMBsFiJoZVih6lSjuhza/X9lh7kDuzOfwAk6s2ca3SxAkfKiSyyQiUlj5wc2ptvUcYdrIX8D23z2M+HcF//crOgvAr7eqBoKSVAHDX4iQA+2LwoDq2ujFNOcht14IZnABY/qJhpeDbbUbOT2kl0C4FZ/DIlRuq54wcWWaxVhA0NR2abvgiNT+5kMZb2zWmsKyOaiuY9/gMQ5CP7CBjgCARMWWStaaG7aoytAy88z1h6voB1mvieQ5xMbSLkVvKxIYqRNKxMEpjRu7mBotHjrlHrhWctJK6fkDzX1pJTLENCpaw4SBFk+M4LGdiODJANz0MSRppJWUdhVegZeSCkAcREEaOJoXt2xsV8FxnYPAbrIzcsbkkeD74kmlSCj4s/AAwfQpeBw10YzohYToh4nOvb+KPX1jFZ06v40tnr+GlS3mc3azgSrGBsqzi2z4O5Hal4EFvvfcqwiEeP/rwATx7IbcjMXK9LZObD3CQO7kvhRDP2Q9yNSVwaSWRJtpVEBBGzu/BybwmEaLAD2XC8gExcgsTUeRrCrVSpyJrSPpQf7LooILASvH1g5Hbb/rkWFi5Qi1YtcAMi7TSQeo3AWHXSGLlsOoBgqQkoErx7JUdMHKAacvpzle4sFUbKKskmIiFb6jUymA0VzcYOp1h9r8+SQhhW6OncJ3Qy6xgDTtpKP5LK2PtYsc6RYSwU8/en/70Q9bAyAJaRi4ofxzQee8NZeRqaqDypdlUO/mMkpE7OB0PjMFMRcNUhwPDMHBmo4J33b0QwFXtxvJUDLKqY6vSRDY1mD32w5/Si0dvmcFffesKvnGxYPu1fgzkVil4Re77862F2k0+yAHAP7lvCb/xhTfwB1+9iP/4njsBABttlseJnNwpYqKAo7NJ20EuXxsBI9dOoM3Vhh94yd8HIa3kOA4L6chQRi5XU8BzdAogN5jrun8foAgu8usetJSJ4StvbMEwDGrFAQnTiPsxyHUFnjx4aIrqe4oNBQlJ8Nw3PAjTCREVWaNSK5EFviNpZcTsr13Lm+9XWo8cjdfaqa3IHC7Ns2xLN/BWrobH27Uwg5COhm+oHrnxIOcAxbqKpCRQhW1IYR4Kg0dOafk/yJFNDA37ZRiGmSYUECNHU0HQUHVHA8C0wwezycjZD3JBMnJCiEdCEoYOcrlaMzDGC+guBbcf5M5slnHH/okArsqEOYzbb+AuFxqoNLXAg04IrNS2fH3kg9x/es+d+Lfvug3VpoaqrKEsa9Z/V2QV1aaGiqwhm5J8qWkgjNygwBPyIB512MleQDoWxrvv3Y9PvrCK//27jyGbMvvJphNioMmQgOmT++wr69B1oy+rrbZ0lGUt8EEuLoYgCbxtcXKupkAUeCsRz2/Mp6ND75m5NnsZ8lkh0K2osBvk1JaOhtryRRVAu8zqBmHk/PDIzSQlzKYkJkauWA/2PEDONrmaYiul7tQ3sZ8zE1II68WGtRSl88iF6TxymjMLT3eYynqxAUXTB5aBE0xERWyW2HyPexnjQc4Byg2VegsshdiklU3V/7ATMijSSCubDqNqWRGzYmQp0o0U9rATN0hGBCgtfei2qyyrFoMQFNLRsI1HTg38sDSXtq8gqMjmRu999y0FdFXma1hu2L+3gvbu9WI50+mSu+9AZuDXlWUV+ylkLW7AcRySkbB5WEv7+k/1RTcj1w9EGnOzSysJPvjIQfzRc5fw8ecu4V985zFcKcqBJlYS3L04gT9+YRVv5Wp9S3kJk5oJOOyE4zgzFMJGgparKpiOB+gtnojgufO5IdfTDMivR+9xrlopzd4fIckya9VmmdUNsmj1q47l9n1ppgqCYsBhPlYpeKVpO8i58si1qwTW8nUkJYFKOkq7RJXVFnOiONDuIG6fG8/bVA8QpGPDz07XG8YeOQcoMrAvJiO3tzxyHGem3TVp/GiK8+0NC4gkok7FyPnv2esGkTEO81iVGmpg6ZAE6Wh4YDdaSzdQrAfvQ5lPR20PAmc2SYF0cGxhKhK2hvFhWNmogOPMHrVRYN9kFBxnMnLDUG163+G01xAVQ0hKAq4NYOQKdQViuyNwDODAdBzfcWIWn3juEmS1hY1iI9DESoK7lkym/eUBxeBB16J0Yyoh2nrkctUmMgH44wgW0lFslmVoA/pmc1XF9+oBoCOtpFFUkGehH4zcUoa9gqDjkfNneLptIY3zW1XqrttCXQ00hInIhmkCT9wNcia7tpqvYzETo1p2JCQBNaVl6/t22qFs/nwyyJlBYYftPHLRMIp11faarheMBzkHKDVUahOrJISoGTlLxujzIAeYH2IajxxJtvTdI0cYOYobpewg7MQNyMNqmLyyFLCUAhjOyJUbKnQjmELSbszb+D2A0bBeNMM4YEo+lzMxX7wWNJCEEBbSUdvUtiCklXsB2SGl4KW6eR8OurttL+NDbzuIQl3FX37zCtaLjZEwcodnEoiLoYE+uUI7hTEzAknsdEKy9ciZIVH+D04ECxNR6MbgUJ98TQlksIyK9KXg5Fnoxz1o34S5zGIb5Mz7ul+M3Ml9aehG59llB5YzohegTWQFOst5Z/UDIdQUDRdzNSpZJWAu6Vu6YasAM6WV7NcUE0Ootz1yF7aqSEfDtgvsiVgYmm5QWXmuB4wHOQdg8UOx9MhpugHDAMQADLKRME8lrXRjjGWBxchRdMk11JYV2BIEyMNq0CCn6wYqTW1PDXL59tY7cEZuwr4UfGWjjIlY2NoABwESRGPndVzZKI9MVkmwlInhUm5wBYFhGL6U3+5FDCsFL9aDPSxdD3jgYAa3LaTwW196EzWlFWj1AEGI53DH/onBg9woGbm4aNu3tV0NOO13gjBh/Qeo7WoT0wFdzxyFogLoZuS8vwdFwiHMpSJsg5zsn0cOMNNYAeC1K3SDXLGuBDzIEUbOPsCDnOmc1g8YBnBxu4alKbpBjjynKs3hS1RZbTlm5AgjSxIr7ZZ7hC29UQJPxoOcA5hGVrobK+mRo6FwiQTTb2kl0GbkKAbMoKSVrIxcJEBGrjME9L8RVZoaDAOBplYCwwc5svUO+rBEDPPD+ohWNio4PpcMlEkhB45BUlTA9Gdeytf3xCA37BBD+hb9rB/YK5gdwsgV6spN3yHXC47j8OFHD1odcgsjGOQAU165slHuq/rI14i3cRTSSpORG/Y8ztcUqzw8CFil4MXd73NFM4NhgkjQBOhLwclCLOXTPWgxE8Nqjn6QIz1lfqkU5lIRTCdEvErhk9N1A6VGsP70SNiUodOkQzbUFsQQ7yg8J9GWruoGsEjZs0oqIao2S1QzVM9B/YAoWJacC9tVHJq2r5giZ7VBHaXXG8aDHCMMw2DqDJMEHrphsm12IBLMQKSVApu0MrDUSoqwk4YSrEfOjpEjw0Hgg9wQw26+PcgFuVkGgLmUeXPf6HMoAUzv3tnNSuDDUopCHntmswLDGF3QCcHSVAzbVWXgZ8FPWdNeQzYVwbVy/4N30PKl6wXvvH0B2bZnZn4EHjnATK7UdGNHrx1BwUobDf61m06IUFsGygPuA3VFQ0NtIROgtHIYI1cIWFlBO8hZzzyfBrllxi65qqxB4Dnfzk4cx+G2BbrAk4qsQTfoeoa9xHSSrhTcDG1z9nuKS51zF00ZONBhSWs2aiunQX9E7lmRVVwtN2075IDOvWfYYvd6wniQY0RDbUFp6dQPIcKu0fjkOoyc/0MKvbTSuZ6aBbRhJ4ZhQNb0gAe54YwcGaZGIa2UVb2vdHdU8qUFG5nQpVwNDbUV+LBE43M8s2nKZo4HWNnQD3Zmf/I+9EtGtJeQTUpoanrfxNFCwPKl6wWiwOPH33YQAs9ZKahB4+7FduDJ2u6Db76mIC6GAq9FALpi2gcceEkQSpCMXCoSRkIS+jJy5GAeRDk5YA5yNKXgfi+TljIxXKs0LUWQHYjU3E+Vx8l9KbxxrWr7u7GevUH3JCZEhkHO2Wev+/Vm8cgBFNJKp4ycZMo9v92uh7ALOgE6g9yNUgo+HuQYwXpoJxsGmuRKciAPKuyEpkfOTcIRC0SBRzjE2TJyastASzcCrx8AKBi5gKVuhAHsx8rlRhQoMGuTfLayYSZW3hr4IGcfdrKyUUYyImA/pWTELyxPDR/kyj7LmvYSSPx4P3llcQT1GtcLfvLRQ/jSLzwRmCSvF9lUBPPpSF+fXKGmjMQfB3QGtEFeotyIlAwLE/1DooiyIiiGcK4t87w6RBoP+B/3T/xXlwt0rFxV1nxfbN2+L42Wblipy4NAhoOgl0xmtQaNR855WByRVnKcmbBMA/LsHSatNAwDiqY7YuTIoEhkr3bVA0C3R248yN2UIC/8BIO0EgBV4EnQHjma+oGOMdb/a+rWOg9CI6DBshsJUQDHYaAcZ5SMHNBfHlCoKYiE+UDTPQH7UvAzm2WEeA5HsvY3Wy9h53MEzCHzxFxq5CmIyxlzozjII1K9iaSVs8n+peCy2kJT06n7PG828DxHLX3yC3ctTuDltcKuP8+PoBaFgKRRDmLk8u1Ey6AH4EGl4EEzhAukFHyANJ6gIquIhkMI+xTMtshYQVBp+j/I3bZglmk+c3ZrqMdyVNJhmo5EwF1YHJFWzqci1EMXeV2GlYITxZrTknLAHOR4rrMIHYYOIzcOO7kpwXpot6SVDOXbwTBye0taCQBxMWTLyFnXE+CAwvMcEuLgUkvC8gR9qEwPYeTyNXUk8d6AWQq+OUBaubJRxqHpeOCyqrgYAs9hYCm4rhs4s1EOtNtuENKxMFIRAZfy/ZMrO7KmG3+IGcTIjUq+NAY97lqcwFq+sWtoKoyQSbVi2mv9D3CE0RgFI9dPjk4YwunAGDkSVjW8gsDv+pODU+Yy6+zV4ewXQTWAOpb9k1HctTiBX//8OTz1+89bUr5elMiyP3BppYRiXYU6oI+QoKHqjsPiSE8fy5KIsLbDznads6+T+oE2I3e5hP2TMaqfEQmHIAm89Vpd7xgPcowgjBxtsIUlrbT5cAGdN/OeSq0MkAGLSfaMXJCDZTeSEWHgEFCypJXBF4J3//vdKNRHJ18aZphf2Qg+6AQwzerJSHjgML5WqKOmBO/dG4TlqThW8/0PU5ZH7iZg5LIDGDlWZcQYweMuyye3U15ZqI2OkSP/7mBGLniPHGAyctvV3d60XLUJgeeQigbzWZ8fkqDZjbKs+hruNRkXcXgmjm+8laf6+moAjBzHcfjTn3oIv/J9t+L19TLe+bGv4H/7s9O7ZKgWIxd42Al5bw9nmWS1hYjDMyZ55jANcpZHbsggpzq3FZGff2G7RhV0QpBul4LfCBgPcowoM+qfWRi5QKWVtKmVRFoZQABLXAzZ1g+MQloJYOgQUGqoCPFc4OETwxm50R2WBsmESnUVV4qNkQ1LyYgwUB5LvHvH98ggt5SJYXVAl1zV56jtvYS4JCAhCQMZubG0cu/i9v1p8Bxwus8gN6qQGiHEYzIWHihBy1WbiIR5a8sfFEhNRG+HW65q3seDkntHxRAmYmHbLjm/GTkAuP/gFF68WECLIvHbDDvx/z0lCjw++MhBPPMLT+InHj2Ev3l5HU/82tP49f9xDvX22YUMB4GnVlpdcsPlle48cgJiYgjHZumVK5LAQ+C5oR65jrTSWSE4wWEKfxzBRCw8llberCAvPEv9AEDnkeuEney91MqIGJBHziailqRYjYKRGxx2oiHlc2JWP1iDXJ+tUqGujEy+NJeOoNRQrQcbwUo7FXJU8sXUkGF8ZaMMngPTA8pPLE3FcLnQ6HuIIcNoIuDD5qiQTUq41sPIkff8WFq5dxETBRydTeJbXYOcoumoNLWRyb6BdpfckLCTqQCrBwgsb1qPvDI3goXcXMq+gqAiq75Lux84mEGlqWFlw76EuxJA2Ek30rEw9NnqqAAAIABJREFUfvl7TuDzP/84/qcTWXz0C2/giV97Gn/6jTXkawqSEQGCT/7BQSCD3BbNIOfw/CQKPD73zx7DBx5epv4ejuOQiAg2Hjn3jBwAJkZuIioOrG+63jAe5BjByr6QNyZNaqUSqEeOlpFrgeMAMYCbUlzay4ycMDA+t9TwV2YyCETKWeoj+RwlI9epINh5GDjTfiAHnVhJMJyRK+PAdDzwcJhBWM7EoOlG3yS7iqwiIQngHRS6Xo/I9ikFL9RHkww3BhvuXprA6bUi9PZCojiiWpRuTMXFwYNcNdgycIL5if79m7la0zqgB4WFiejA+hiCYBi5DADgBQp5ZbWpjkShsDQVw2/98D34i595GPsno/jFv3gF//35SyNZMM0QRs6mFLzhon4AMGWVrGRDQho+yBFSwcnZN9Y9yFGUgROkY2Np5U2LYt0sA6dlX1h65IIMO5HCITQ13XrADoLcTjgKgm2iSa0kEtWgD9ypaHggI1diKIj3EkKIR0ISdm2VFE1HRdZGNsiRUvBeec7KRgWZuIiZ5Ggi0ZOR8MAC0JXN8p7xxwGdjp61PqltQRyi9hKyyQiu9RxOiDJizMjtbdy1OIGyrOGttkw4H3DBdT9MJyVs1wZ75IIOOgFMXzGwu38zXwt+sDTDquw8cprvnvCFiSgWM1HbQU5t6ZBVfaS9mvcuT+IvfuZh/NYP34P9kzEcG0EXKfHI2VUQyKoe+CI8IQk20krnC/puZQpNhxzBRDR8wzByN89pwCOUGiqTiZVsLtgKwf0f5Ai13tT0oUORrA7/ey8Rl+xTKzuMXLA7iKHSSlkdWadXus/NaNRbb8LI9bJJ5rCUHFm8fyoqoLKx+zWsyCrW8g2899TiCK6qP0iP0qV8HQ/3/F0QCW17CbMpCVfLMgzDsN47pboKSeBHUio9Bj3uWpwEALy8WsThmQQKtdFLYqfj4kDWIldt4ugI5NWRcAiZuIgrvYxcNXhlxXwqgly7FHzQ5yuoZ979B6bwpbPXdnz2e0HODKMc5ABTQvjOO+bxzjvmh9YT+IWYaPrXbD1ySivw85MdI9d0xciFrH+DZUk8MWbkbl6wyuhIUz2dR855BCsryAfZTl7ZcJFwxIqYKNgPciPzyJn+qn436FExcoDJFPYOctbWe0SHJVIK3r3V1Vo6zm6aPW2jQioS7lsIfrZd8LqXGLn5dBThEIdLfbrkKk3//Sl7CdlkBLKq70g9K9RHF5gxBj2OZBOIiyErubKwBxi5qYSEsqztsjsYhoFcTbEqCoJGbwWBrLZQbWqBSyuJzHNQKXhTa0HR9ECWSQ8czCBfU/DmterAr/G7nNwJRrWsnE5I2KKQVgZ9frLzyJEEdcnBdYVDPESBx6GZONPvfSImoqG2qCxGex3jQY4RpYbKdIAg3jI6Rs58QwVVPwDAtoJg2FbOa8TFEOpqa6jck1zvKMJO1JbR93Usj8gjBwDpqLBLLkgitCfjo7kmsl1e7xrkLuZqaGr6SIelVPth0vv+Imb6vTTIhXgO+ydjA6WVo94+B4lsyjzIXus6WBZH2EU2Bj1CPIfb96dx+rI5yFn3phEO4USqmO/pkqspZsn8SNN+uxg5cn2BM3Lp/h5ngiB7LIlP7vkh8korxfcmuicOwnRCHMrIqS0dmm6MRlpJwcg5ZQpTkTBTYiXQqRAbZLe4njAe5BjByr4QRo4q7KQVZI8cYeSGX1eQeuq4JMAwhg+XhJFzsrlxA/LQ6mV0DMMwUysD6vnpRT9pJZEvjXLrPd9TCk7i/Uc5LCUjYRgGUO0J1Pn2RgXpaNg6wOwVLGVifUvBbzZpZTbZLgXvSq4kXuUx9j7uWpzEykYZstpCoT2cBF2W3I1BMe15UgYeMANGsJCO7EitzI2onHxugF+PoDPI+X8PWp6KYTYlDfXJkQFhLzFyo8J0Qho6yI2qh9feI+dOjfbR992Ff/YdtzB9z8SQ+qbrDeNBjhHFun8eOTc6YVaQXjg7Wtlk5AKSVrY3arUhFQSjuhERY3evT05WdSgtfWSHyn6D3KillcDuUvCVjTIEnsPhLL0Z2WuQYbv3NTwzYu/eIJhdcrsZubKs3VzSyjYjd7UrubLYGF29xhhsuGtxAmrLwOvrZeTrCpKSEMiychCIdLL3wEsCUEYRdgKYksaKrFkVKTlyPUFLK20ZOfP6gvDIcRyH+w9O4YW38gN9Z2RAuJlUCoMwnZSGhp1YvcABh8XZp1Y6rx8AgEeOTGN5iu1sQZR1xfEgd3NB1w2UZUZGjqFHTmnp4DhACCBW3JJWUg1ywUkrAezqH+tGQ20hxHMIh4I9dJPtYy8NT4aovTTIFWqjj/juLQVf2SjjSDYRiP9zEMjw090lp+sGzm5WcHyE3r1BWJ6KoSxrVngNgdnhdPMcWojnspeRG3vkrg/cvTQBAHh5rYhCTRnpfQmA1RPXW0HQYeRGJa3cOUCNipGLiQLS0cGl4OVGcIwcYMorN8sy1vIDGMJmsNezlzGdkFCoK9Ba/YkDqxc44EVKImImkg8qdw8ysZ1gImp+rm6EwJPxIMeAiqzBMIA0wyaYeORopJVNTYck8IEwAxKttFILzhgbE2kYOR3RcDB1CN3oDAE7h8xygNvJfkhHw2iorR3vL1JIGg64kLQbvaXgKxuVkXvQOsN45zW8lK+jrrRG1m03DIvtCoLuwBNF09HU9JvKD5KQzDS2q+1BzjCM9iA3ZuSuB8ymIphPR8xBrq6OfpBrD2q5ngoC8r9HJUnf1w4ZIWm/HUZuNHUI68XhjFxQqoAHLJ9cru/fdxi58WJnJiHCMHb7PwksRdMIGDkAA3uC3dQPOIXFyNWH1zVcDxgPcgxwwr7wbfaItn4giOJtgD7spKEEyMhJdIxc0NG5QGcI6B3k9gIj130dwGjLwAm6t8uFmoLNsowT88HHencj1YeR24tBJwTL7QqC1a7Ak+pNun2eTUWsUvCG2oLS0seM3HWEuxbNYvBCXUFmxK9bQhIgCfwuRi5XIwzYaDxyVik4YeRqCsR2V2jg15KOYLM8eo8cAByZSWAyFh4YeFJtmvfzsUcOVvz+1gCfnFXfFLAyhryHB/nk3BSCO0U6NvbI3ZQgJbQsHjnA9Mk1bZgvwNxKBBXiQVg22aaAW1Z1i73zGxYjN+Sa5AAHy270k+UBZp8VMLpBLtVnkCvUR+8fmk93SsFXNvfGsGQxcj2DHM8Bt8yyJV4FAVIK3j3Ikfdf4ibyyAHmAYWUghfanznW+/AYo8OdixNYzdfx1nZt5PcmjuPaoRA9g1xVQUwMBc5WEMwmJfAcsEEYuapZBj4K7+5cOjpYWhmwCoXnOdx3IDMw8KQqa+A4IDbulOwK8unPMln1TUEzcu1n7yCfXFMzLTNCgCqihCiA58bSypsOFvvCuFGUBB5Ki65Hbq8xcs0ApZUWIzfEFDuKDhRgcNiJ9VAbM3I7QBi59WLDSqwctQ+NvEbdr+HKRgWHZhJ7slg6JgqYTkg7Ak+C3obvFcymIlb9AJHCjKWV1w/uWjR9chVZG7m0EjDlirtSK2vKyPxxACCEeGSTEau2ZZTXs5COYLuq9PX2j6K37YFDU1jN1/smaVaamnkoDyBbYK/DGuQGdMnJmruYf6ewGLlBg5yqB+7b43mub8bA9YjxIMeABw9N4YVffjvu2J9m+j5R4KkYOaXtkQsCtPUDgUoraRg5tTWSjWlcFMBxfRi5PSKt7A5hKdRGz8iRCOvNkoyVjTKmE5Il+xgV+gXWrGyUR84UDsPy1M4Kgpt1kMu2GTnijwMwllZeR7h9XxrknD3qJRNgBoj0euS2q82RySoJ5iciHY9ctYnMiK6H3L+vlnYPBGVZRUISEApwcCI+uX6sXFXWxrLKNqaT/as1CAgjN4oeOWCItDJANVo3JmLiOLXyZkM4xCObijAn70kCT1c/oOmBxTJT1w9oenD1A5SplUHruwFze5OQBJQHeORSI3qQ9GXk6goyIyoDJyCl4BtluT0sjdYfB5gSZ0ngrWGo1FBxpdjYE9c2CL0VBEFGf+8lzKYk1JUWqk3NGuRGvawYgx5xScDRWfNzthdet+mEtDu1sqaMrHqAYGGik/a7XVUw/f+3d+cxk+T3Xcc/v6rqqn66+zlm5pnZmT1mvXbWVy47nqzthFh27AUnBJw/IIeCsiFYRoSIBAjBECQuIRmFI0igSMaBbAiCQAjYAoTiLAEhQZw4GMWOHXuT2LF3PXvNzvkcff74o+pX3f083f08z/S4fr96+v2SrHmOtrvcTx/1re/lcTm5pKm9ds5tD3ssX3dpQ50smR3IdQesHii001jNRjQ3kHMZ1sr3yB1VWtmvLokxaXOtwbATHE+WxMdbCF5pRs4FcvOPqz8caTiyFZZWHj21cq8/qnwHirPRbBwurdwbqJ3GldZ2TzoYyO31htrvj4IoX7q40dSXXt7V08/fCWYq5HqzUQbjvxPwoBPn8tmWrt7aLz+Ab6/ozqRyKfjt7rhXmYxcrbg1BL4vMkn5brZrd3pTu8lcT5pP92/mGTlrrdcS+Utb44qKg3ysP4kjoyuvODM/kCMjJ2l+/6cTakauOxh5aW/YalFaiWNKk+hYe+S6g2Fle7ZcwLgoI1dOOKroBZYlkSIj7SxaHNkbas3D1EopL2ebVVrpq6xSOjzsxC0D931lWZLu32rq41+4rt5wFEywtNFMyr7G33ku790LJcic5eFzLVkrPXM9vzK+qlMry6Xgt/bLjJzP1x1O7usfzAO5EHobtzupesNReVFnHDh5Lq3cXFN3MNKXb+5rrz+sfBm4c3Fj/lLwPCNX/WvvsUfO6ukX7ujagWzT7X0ycpPyQG5Oj1zfT0ZuvVgNMS8jt98fesnIba01GHaC48mHnRxz/UBFT+YoMkqTaOGwE/eir6p22RijdprM3TUiVbvX7qA8kDtcWulr0ImUl/u203gcyBVX4kIoX7q42SwvBrw2kPLF9bVxVvUzV2/pTKuhC5579xY5OLlyPLVytU5cXEbuxdtd3djtaa0RBzmgBvN9+9dd0g+/46vKzJxP5S654oT3dneg3nCkbd8ZuSIT9slnbkryt5y8nSXaaCYzh4vc2u97aSV48yPnJEm/8YXprNydbvWlniHb7mR6cc6wk72+G3ZS7XunG2Q3f2qln9LKrVZKaSWOJ2scb9hJ1U/m5hFDWNzvqgyc2lmi3UWllZ7WD0iuLG/66s2tfb+BnKSpyUsuIxfCQAHXZ5HGkV51Pozx/hvNpBx24gad+BjvfVyX3S65ay6QGyhNosoy96GYzMhd3+1TVllDG82GfuyPvCaI566b7ud2x7l+Od/vm/cXu+Q++ewNSX4rKyb79Sb5ysh97QObajaiQ/vk7pCRm3J+PZ1fWukuzlccNCVxpGYjWrh+wMewk421vNViOLJH3zhgBHIVSOPjDTupMiMn5btE9hZMiByXVlZ3TK0sXpiRyxeCh5ORu+W5tFLK34xcIHe9ODEJoUfOrSD4qgsdNTz1EB6U9zn2NRxZffb528GUfM5zvpNprRHrD4pA7tb+wNtgHZ/Ws0RrjVgv3Orqxm4/iPI81JebTukyci8XEyx9lTI67uLXp57N+3d9Hs/FzeacHjk/GbA0ifQNlw/3yeXDTriw42x3Mr28050ZnHSLEkYfqxo62eEZA86+p2EnW2uz9wPXTRhnV6fcsYedDKsN5JqN+FillVVOiWyniXYDXD8ghdkjJx3IyBWB3NkATnTdCOuQgqX1Zj559AvXdrTfD6d3bx5jTD65siitzMuIVu+kxRijCxv5CoKbez2WgWMproTyxSJz4TIYvnuLz7VTpXGkTz170/vxXNpsHiqttNYWw078vP4ee+SsPn31VlkZMxpZhp0csN3JNLLS9Rklg3uez5/mzT/Iq9H8DDuR6r8UnECuAlnjmMNOKr4q0UzixcNOioCqyhd+K43nvtgHw5H6Q+tl/YCUl1be3h9MTTq7tdf3Pgp+c61Rlgte3+0pMv4WlE966ExeFvj6+8MJljbW8ozcZ4qJla+9GEbv3iKXz7X0xWKXnI+JcaG4b71ZllaeCWDyIerLVSyMM3JFIOe5Ry6KjC5uNsuST5/Hc2lz7dBS8O4g/wz29R702CNnZa30m1+4Lkll9c46pZWlcin4jIEn+31/MwbaWbywtLLqJeXSRCBX88mVBHIVOHZpZeUZuWjh+oH9wai8XVXa2fyMnDuetdTP03aj2dBgZMvHrD8caac3DC4jt9VKK13WOs9DZ1v66e/7Bn3PNz7k+1BK61mi/f5In3zmppLI6NH7wujdW8Rl5PKr4avbD3J+IyuGnfS1ueY/44z6asSRzrQaZW+cC+h898hJ45L0tUasVurvtT5rKbi7YOjrQuEbHzqjRmzKPjkXGLRX9D1xFpdtfun2rIycnzH/Ur6CYO76gb6fjJz7HKn7wBMCuQpkjehYpZV5/XJ1T+assTgjV06trPCYWun8HrkyQ+ixR04a11O7D7XNNb8fIpOB3PXdns4ENAji2772UlAfsu5v+LHPv6xXne8EMXjhKA+fa2m/P9KLt7u646k/JQT3rTf13K39vLQyoOc46ulcJ9O1ojfu2k5P61kSxPvBA8XAE99B5f1Fv95keaVb1+CrT3ctjfX1D27p1z9/TdJ4LxmllWPb64szcv4CuYZuLxx24i8jV/ddcgRyFUjjONCMXFxmuWYpd45UWFrZTudPrdyveK/dQe4E2n2YlR9qAWTkdntD9YcjvbzTKxv5cZj7W33q2Zt6XSArEY7y0MQKAp/9Kb5d2MiK57kN6mIF6ulcOy2zFtfu9HTWc1ml45Zx+16F4DJyz90aDzxxFzF9Xkx67JGz+q1nbmq3NygDA0orx44qrfRRwigd0SPXH3lpmXHVVPTI4UjH6ZEbjaz6Q+th/cAxhp1UGDgtmlrpO5BzvXDuw+zmXhiLiTcnriq9vNOjf2gBFwQNRjb4QSfOw0Ug9wfXdle6tPK+jfEFii1KK7Gk7U6ml3bGPXK+B504bnKl74ycK/H88o3JQK4InDxeTHrskbMajKw+8cUbZORm2GgmSuNIL84I5PZ6ofbIjbxk5Ny5Gxk5HClLIvWHVqMFuyrcwvDKM3ILA7miR67CY3JTKycHijhuHYL/0sr8zSiYQG5tMpDrez8BCNlkSdBraxLIPXimJWOkL1zb0Z3eaq4fkMZLwSVRWomlbXfSskfupTtdnQ2kksEtBfe9CsEtBX9uorRyHMj5ew9608NnFJm8PN5leFb14tYsxhhtd9KZPXL7A7+llbN65IYjq97Qz/qBRhypkyVk5HA0F5y5YG0WV3qZVrhva60Rl8HRLHseSitbWazhyM4sRfUxRXOSuwp560CPnO/Syo2J8oC8R45Abp7JK8l1Ka1Mk0j3b67pM1dvy1q/V8N9urA+kZHjOY4lnetkurnXV2+Ql6T7LmV0XEbO9wRNKT+WyaXg7rPP56Tm9WZDX33/pn7989fK0koCuWnb61lwGbn1ZqLecHSoOq1XDtXzc1ybaw3d2GPYCY7gGqgX9cm5J3eV2+2PnFrpaY+cpJm11PueX/ChZ+Seub6r4ciSkVtgoxhMs91JpzI8obt8tqVPfznfLbWqZUQXNsZ/L3rksCwXKF3b6erlnV4w75sPnllTmkR6sFjf4tPFzeZUIBdCj5wkvfmRs/rEF2+UayN8H09otjuZXro9q0fO79RKSdo5MAOhPPf1kJGT8uqOm2TkcBT3BF3UJ+euSmQVZuSOU1qZxpGiCkfZuwmHs1YQuIycz2ZdaWJqZQBXJ6VxIPeFl/Kl0WTk5nPZrLr0xzmXz7b05eKEalVPWjaaSfleukkghyW5oVCff3FHg5H1XsrorDcb+uUffZu+68qDvg9F928dDOQGMmZ8wdWXxx45q+5gpP/9e/n0ypAmI4dgu5MGN+zE/Y0Olle6ZIKvibFbrQZ75HA0V1rZXZD9ctm6Khs+s0Y+TXNWP5rk50XfLsomZw082ffcI9dOExkznZFL48jbG6NTBnLX8qXRoVxZDlE+YjzSV9+/6ftQTuTyufHV+VUtrTTG6L4iK8ewEyzr/Hr+HPrs87clKZhhJ5L0iu12EKsQLm6s6aU73fJCsxu2VOXF3Vm+8RVnJUm/9nvX1GxEalR4AbwOtjuZru30Ds1l8LkQ3GXkbnengyaX4PB1HrW1lrJHDkfLjtEj1/PQI+deOPNKPn3sHGnNSb9Lfnr2JkWRUSdLykDu1l5fG2sNGeP3Q80Fcp9/KQ/kzgR0QhKaKDL6hT/7Vv25t7/K96GcyMNTgdzqXn2+sJ6pncaVDoXC6eQycp97/k7+fQA9aaFxkyufL1YQ3Nrve69AkfLPuNfct67ecKRO5v94QrPdyTQc2alMk7VWex73yLnPrYMZuTKJ4enCxcbEHt664tOwAmWPXGAZOdf7Nq+80kcg5zJyuwFm5KS8jHI87GRQ9lz51IgjtdK4zMiFdGU5RG94aMt7X+NJXT47EcitcBnRpa21YPZ9od5c4Pa5IiNHJcNhbqedK6+8tTcI5kLSY4/kWblQjicks5aC94Yjjay/C+Flj1zvYGllAD1ye/25lWl1QCBXgZP0yKVxlcNOXCA3O8Dc85CGb6VHZ+R8XVGS8g+NydLKUAKCzbVGOUKXjNzp8/DZdvn1qpZWStJfevzV+qnvfoPvw8Ap0MkSpUmkzz2XB3LbgfTIhcRl5K4WKwhuB5KRk8aBHBMrD3MTWCcHnox70fz2yN2el5HzVlrZUH9oZ85lqAsCuQqUpZULplaWgVyle+Ty+5qfkRtV3yOXLcjI9fxeuZHyjNzkQvCQAjkpL81te7rihq+czVaj3B+3ylegH9lu600Pn/V9GDgFjDE638nKEfYMiTrsYrEKwWXkbu+Hk5F7M4HcXOeLixKTKwj2PbemlKWVByaSu0o1Xxfo3U7SOg88WeqM2Bhz1hjzUWPM08W/Z2bc5g3GmP9jjPltY8xvGWO+e5n7rKPsiF60/HfVByku2zZvl9x+f1jpOgRpIiM3a2plkSH02ZM2mZELpV9AGu+SO9P237OHr4yHz7UVGalFoA7cE668cqOZ0Hc5QydLtN5M9JwL5Lr9YAK5CxtNPXqho/PrZFIPOl+WVo6HePhuTRmvHwirtHKzGJxV54Enyz5y75f0lLX2UUlPFd8ftCvp+621Xy3p3ZJ+yhizteT91oorl1wUyPnJyB3dI1f1i77MyM3aI+chQ3hQyKWVEleVT7PL51rqZAmBOnCPuH7iUFYPhOjSZlNfvpGXVuZ94WF85knSkz/4mP7mH3u978MIzuZaQ43YTPXI+W5NaaWxjAlv2InLyNV5l9yyl1beI+ntxddPSvofkv7q5A2stZ+b+PrLxpgXJJ2XdGPJ+64Nl5FbVFo5fjJXuX7AlVbOm1pZfeDUTPIX+6KMnE/rxbCT0cjqVoCBHA37p9f3v+VhfePDh4oeANwlF8AxIGq+S5treu7Wvqy1utMNp7RSku7fWvN9CEEyxuhcO5vZI+frHMoYo06alKXMju/1A+7cqc6llcu+Iu+z1l6VJGvtVWPMhUU3NsY8JimV9Htzfv8+Se+TpMuXLy95aOFwKwWONezER0ZuznHtD6qfWhlFRq1GfCj9LuWBXNNzWZnLyN3pDTSyCmJqpTSRkeOE5NR68yvP6c2vPOf7MIBTww044QLYfJc2m/r01Vva7Q01HNmVHrZUJ9vr00vB99yMAY9VTZ1mEuRCcEm1XkFw5FmoMeZXJF2c8aufOMkdGWMuSfpXkp6w1s5MAVlrPyjpg5J05cqV+s4CPeBkPXIVTq0s1yLMDuT2en4yYK0smTnspBtIRm44snqh2KsTXEaO0koAOBY33Y/Syvkubjb10p2uXt7Je4hCyshhvu1ONt0jN/C/vqmTJYfWD/iYDzFpq+yRO8WBnLX2XfN+Z4x53hhzqcjGXZL0wpzbbUj6L5L+hrX21+76aGvKBWfHKa30M7UynIXgUr5Lbt76AZ+rB6Txh9iXruc9A8EFclxZBoBjccNOttlNONf9m2uyVvrdF/LF6WTk6mG7k+mzxWoNaTz12+c5VGdixoDjzn19HVezESlNIt3YW91hJx+R9ETx9ROSPnzwBsaYVNJ/lPRz1tp/v+T91VJ6nD1yw+p75I4cdjIYeUnDt+dk5HxlCCe5Ru9nikAulKmVBHIAcDLn2pRWHuVisUvus8Xi9A0ycrWw3cl07U6vXHS953lqpZRn5A6uH3Dnn76mxhpjtLXWqPWwk2UfuQ9IetwY87Skx4vvZYy5Yoz5UHGb75L0Nkk/YIz5f8V/Vmqj63H2yLldGq6frgqLArnhyKo3GHl50bfTZE5GbhRMRu5ZF8gFlpGjRw4AjsctvL640fR8JOFyj5FbnE5Grh62O6l6w5Fu7eWBUznsxOOcgU52uEeuOxipERvFkb9pzFutxukurVzEWntN0jtn/Pzjkt5bfP3zkn5+mfupuyQyiswR6weG+ZM5qvDJPN4jd/i4xpOEfPTIxbq+czjN3e0Pvb4JSeOrkc9c35UUTmnlI9ttNWKjRy90fB8KANTCo/et6+d+8DF906sYIjTPpWIy5OdeICNXJ26X3It3utpsNcbrBzwNFZGKHrkZC8F9HpOU98mtcmkljsEYozSJFg876Y8qn9rjMoWzMnLu6k3TQ7q7nSZz1w/4OJ5J7mrkM4Fl5F6x3dan/8679bpLG74PBQBq422vPq+kwkqYuulkidazhB65mnETWd3kSnee10z9Tq2ctX7A5yRNKT+Pu7l3uJ2nLnj3qkiWxAtLK3vDYeU1wlGUB5iz1g+U9dQeMmCtNJ65EHwvgIxcWVp5Y0/GSOtZOFcnG5yMAADusUtbzfLiLlMr62FWIGdMte07B7keOde3lx9X9UmMg7ZaDd3cJSOHI2RJtHDYSZ6Rq/7P0Uy9zCmFAAAa9klEQVSisj9vUnn1xkePXDYnIxfAsBN3NfLF211tNBuVlsICAFC1i5t5eWUcGbU8X0zF8bhJrG4p+H6xvskYf+csnSyRtdLuxPldCBm5rbVGrReCE8hVJJ0TMDm94cjL1J5mI55TWln9XjunlcaHplaORlbdgf9hJ+00lovdQlkGDgDAV8qlYhjMejPxGgjg+M60UsWRKXfJhbC+qVNkcyf75LqDMDJyu73hwmRLyAjkKpIlkbrDBYHcYOQl5X1UIOejlLGdJeoP7VQpqu9dI44xRp2inDKUQScAAHylXNoaB3KohygyOttOy9LKvZ6fKeST3LnTZJ/cfn/obRm4s9nKs5c3a5qVI5CrSJrECzNyXU8725qNaOZCcJ/DTlzpxmRWbrwDxf9T1pVXEsgBAE47t4JgPeMzr062O9m4R24wVNPz+ZML5CZXEOSVVv5LKyXVdpec/7PiFXFUj5zXjNyM4/LaI5cWL/bujEAugPp8d1UylGXgAAB8pbgeOTJy9bLdSfWi65HrBVBamR0+twuhtNJdlK9rnxyBXEWyJFq8EHww9PJkbjZi7c0Z9S95mlqZuYzc+Lh8BpYHuZUDZOQAAKfd/UVGLpR1Ozie852s7JHbH/gfFud65KYCuQBKK7daZORwDEftkesNPA47mXFc49JKfxm5yYZYF2wGEci5jBwfagCAU+7iJj1ydbS9nunFO11Za7UXQEbOleYeLq30vxBcIiOHIxy1Ry5PL/taP7CgtNLD8sh2kX6flZHzfUVJokcOALA61psNXVjPyl451MN2J1VvMNLt7kD7ff8BU7uotgotI7dZZORu1HSXHJdXKpI1jtEjF+D6AR8vfDfsZCf0HjkCOQDACvjwD38zFy9rplwKfrur/X4Aw05mlFbuexr0N2k9SxSZ+k6tJJCrSBYvLq3segvk5k2tLAI5H6WVMzNy/ko9DxoPO+HlAwA4/S4VA09QH2Ugd6envb7/HrksiZXG0YyMnN/jiiKjzbWGbtAjh0WyxlHDTvxM7pk/tXKkODJqxNUv/2y7jNys9QMeSj0PorQSAACEbBzIuYyc/wvh7SwObv2AJG21UnrksFiWxEcMO/FTJzyvtHKvP1QziWRM9YFcy2XkuhMZuYCGnbiMHIEcAAAI0fZ6PsTjpTvdPCMXQGtKp5mUGbnBcKTByHrPyEl5q0xdSysJ5CqSHrFHzuewk/3+SNbaqZ/7vHrj0v+TGTmXNfRdGiBJrzrfUZZEeuAMpSYAACA8Z1upjJFevN0NYtiJJHWyRhnIueSG72EnUr4U/GZNh534f/RWhNsjdzBgkiRrrXpDTz1yxRWag9lCny/6ODJaa8RTPXIhrR94yyvP6bf+1h/WhXUmeAEAgPAkcaSzrVTP3tiTpCBKGNezpCytdOedIZzXbbUalFZisSyJNLLSYHQ4kOsPraz1c1XCDQ85WF7pe8JRO4tnTq0M4QUvKYhSAAAAgHnOr2d65uU8kAuhoqmdxWVGzp13hpKRY9gJFnLZtll9cr3haOo2VXKB0cHJlb4bY1tpciiQS5NIcVR9zx4AAEDdbHcyfen6rqQwLoR3mjNKKwPIFG62Ut3a72s4I9kSOv+P3opwGZxZkyvdz9LYz/oBaUZGbuB3VG0rjbUzUVrZ7Y+CuJoEAABQB9udVM/d2pcURkaukyUTgZy/NVcHba01ZK10e79+WTkCuYqMM3KHB564n2UeXmRlRu7Ace31/Gbk2lmi3cn1Az3/yywBAADqYruTyY1mCOEcar057pFzlWBBZOSKKeR1LK/0/+itCFcD3J2xfDuMjNysYSc+e+QS7UysHwhhmSUAAEBdbK9n5dchlFa200R7/aEGw5G6ZY+c/+PaauWBXB1XEBDIVaQsrRweDuR81gnPHXYy8JyRS+PpjFwgyywBAADqwC0FlwIprSz28O50hxNTK/2HIi6Qq+PkSv+P3opIA83IZY05gZzn0sp82MnEQnACOQAAgGPb7qTl1yGcQ61neSB3pzeYmFrp/7g21/LH6UYNd8kRyFXElVb2hqH1yM0bduK7tHI6I7dPaSUAAMCxTWXkUv/nUC4jd2d/ENZCcEorcZRFPXJdjxm5tQXrB/xOrUymplbu9YdBvAkBAADUwfnJHrkAMl9tl5Hr9oNaCM6wExxp4R65QQh75MZBk7XWe09aO43VG4zUL3oK93pk5AAAAI7rbHuitDL1f8rfKQK52/uDcTVaABm5RhypkyUEcpjP1QDPCuR8ppdnBXK94UjW+r1K0ipe7LtFVm6/PwpiRC0AAEAdNOJIZ4qywRAyX+sTw07K9QMBZAqlPCtHaSXmckHIrD1yPa+BXNEjNxFg7vf8p7vbRRml65PzXeoJAABQN65PLoRzqM5UaaWbDxFGKJIHcgw7wRyu/21xRs7DsJMZ6wfccnCfw05cRm6nmwdy7JEDAAA4me1OpiQyaniYw3BQe7K0sh/OsBMpH3hCaSXmclcceoH1yEWRURpHU8NOXFDnszHWZeR2usOyZ49hJwAAAMe3vZ4FUVYpTWbkBtofDJUmkYwxno8qt9Vq1HKPXOL7AFbF4h45vw2fWSOaysjtFV/7DJxaaZGR6w2C6NkDAACom2961Tl1+4fbenyII6NWGmunO1B/aNUMJBsn5bvk6piRI5CrSLl+YEGPnI+MnJQHSJPH5bJzvvfISdJudxhEzx4AAEDdfO9jl/W9j132fRilTpboTncgyXjZnzzPVivvkbPWBpMlPI5wQuFTzvXIhVZaKeUNsHu9yUAugNLKbJyRKzOEAb3gAQAAcDKdLCl65IbB9MdJ+bCT/tCW55x1Ec4jeMpFkVEjNnOHnURGSiI/VwCajekeOfckbnosrWyn4/UD+2WpJ09XAACAuuo0E+10B+oORkFVWm3VdCk4pZUVypJ4dkZuOPLa8NlsxOWkSkllLbXPjFwrc8NOxhk5n8cDAACA5bjSyjgyQWXk7t9a09c9uKnB0Po+lBMhkKtQlkQze+Ty9LK/IKWZxNPrBwLokWs13B65YRAZQgAAACynkyX64su7ypI4qEDuba8+r7e9+rzvwzixcB7BFZAmUbk3Y5LLyPmSzSmt9Dm1MokjZUmknd5A+z165AAAAOrOZeS6A79JjNOCQK5CWRKpN5zRI9cfeb0q0WwczMiFUcrYzpJ8amW5oJwXPAAAQF1N98gRhiyLR7BCWRLPzMh1PWfk8vUDkwvBwxj330rjfGplsX6AjBwAAEB9uYzcvue2otOCQK5C6Zweud5gVK4n8KGZzF4I7rt2uZ3mGTnWDwAAANRfp5moP7S6tTdQRkZuaTyCFZpbWjkYeV2KuJbGU3sz3G6PyNM6BKeVxVN75JqsHwAAAKitTrEn+NpO13sLz2nAmXGFssacYSeDoTKfGbkZPXK+yyqlPCO30x2M1yEEcEwAAAC4Oy6Q6w8tGbl7gEewQmkczV0I7vPJnJdWjmRtvjtjrz8Mooyxlcb5+gGmVgIAANSeC+Qk/y08pwGPYIXmLgT33CPnyjpdkLnfD2OSUDtLytLKJDJqeHyMAAAAsJxOcxzIUWm1PM6MKzRv2El34H9qpaSy7DOY0sosLoedkI0DAACoNzJy9xaPYIWyZHZpZW/ge49cft9uX9teKIFcmmfk9vt+h8EAAABgedOBHOd2yyKQq1DWiOaXVvoM5IoXkht40g2ktLKVJtrvj7TTHWiNiZUAAAC1Nl1aybndsngEK5TG8ZxhJ36XIrrsm1sEvj8IJCOX5cfw8k6P0koAAICaW88a5ddk5JZHIFehUDNyLtvl9rXt9cLoSWulbtcIgRwAAEDdNRuR3Jpi1g8sj0ewQm4h+Ghkp37e9d0jd6C0MrSM3LU7XXrkAAAAas4YU/bJkZFbHoFchVzWrTccZ+WGI6vByHrNyGWNA4FcQD1yEqWVAAAAp8V6My+vJCO3PB7BCrkrD5N9cq7U0u/6gWJqpeuR6wWSkUvzYxiMLIEcAADAKTDOyBGGLItHsELuCTu5S84FciEMO3HHFUppZStjshEAAMBp4lpnQjjXrDvOjivksm5u8bYkdYfDqd/50JworRwMR+oPbdk355PLyEnSWur/eAAAALCcjiutJCO3NB7BCmUzeuRcUOd32Mm4tHK/yBCGsLdtOiNHIAcAAFB36ww7uWeWOls3xpw1xnzUGPN08e+ZBbfdMMY8a4z5p8vcZ52VPXITGTkX1HkN5CYycm7gSQiBUycdB3L0yAEAANSf65GjbWZ5yz6C75f0lLX2UUlPFd/P83cl/c8l76/WZvXIBZGRK4KkvclALoCrJJPllCEElgAAAFhOm4zcPbNs9PAeSU8WXz8p6Ttn3cgY8yZJ90n65SXvr9bK0srB4Yyczx65ODJK4ygvrXSBXAA9aWkSKY3zx4WMHAAAQP11mkUgR0Zuacs+gvdZa69KUvHvhYM3MMZEkv6hpL+y5H3VXjnsZNb6gdhvoJI1oqK0Mj+eZiANqC032SiAwBIAAADLeePlLb3p4TNqT7TQ4O4c+QgaY35F0sUZv/qJY97HD0n6r9baLxljjrqv90l6nyRdvnz5mP/z9eFSyJMZOVdm6fuqRLMRqzsIq0dOktppohu7fTJyAAAAp8A7XnNB73jNodwP7sKRgZy19l3zfmeMed4Yc8lae9UYc0nSCzNu9lZJ32KM+SFJHUmpMeaOtfZQP5219oOSPihJV65cscf9P1EXLlibnZHzHcjlpZV7RSAXyrj/Vup2jYSRIQQAAABCsGxO8yOSnpD0geLfDx+8gbX2+9zXxpgfkHRlVhC3ClywNjXsxC0E952RS+IDpZWBBHJFQywZOQAAAGBs2ejhA5IeN8Y8Lenx4nsZY64YYz607MGdNi5Y6wWZkYsPrB8IIwPmloITyAEAAABjS2XkrLXXJL1zxs8/Lum9M37+s5J+dpn7rLNyj9zMHjm/gcrB0spQeuRaRSMsw04AAACAsTDSLisinbFHLqSM3F5/qG5ggVzbTa0MpNQTAAAACAGBXIVm7ZFz2Tmfe+SkydLKokcukNJKl5ELZfgKAAAAEIIwztZXRBIZReZgaWUx7CSAQK47CK+0kh45AAAA4DACuQoZY5QmUZjrB5KoHHaSREYNz8fjtIuplaFkCAEAAIAQcHZcsSyJD5VWpnGkKFq8LP0rbbK0MpRsnCS97tKGXnm+rU627KYMAAAA4PTg7LhiWRIdGnbiuz9Omp5aGVIg9+6vuah3f81F34cBAAAABMV/BLFi0iRStz+9fsB3f5xUZOQG+dRKyhgBAACAsHHGXrEsidQdTvfIhZGRi2WtdGu/H1RGDgAAAMBh/iOIFZMm8VRGrjcMJ5CTpOu7fSZEAgAAAIHzH0GsmCyJ1JvIyHX7o0BKK/NjuLHbo7QSAAAACBxn7BXLkkjd/sSwk1AyckmehbuxS2klAAAAEDr/EcSKObhHLh924j9wcsHbjT0COQAAACB0BHIVO7hHrlfskfPNlVMOR5ZADgAAAAic/whixWSN6T1y3cFIWQA9aZPBWzOAUk8AAAAA83HGXrEsni6tDC0jJ0lrKRk5AAAAIGT+I4gVkzWiw6WVAWTAJvv0KK0EAAAAwuY/glgxWRIfGHYyCmLYyWQWjtJKAAAAIGycsVcsn1o53SMXQkZuqkeO0koAAAAgaP4jiBWTJXlppbVWkls/4P/PMJmFawaQIQQAAAAwn/8IYsWkcaSRlQajPJDrDUZhBHINeuQAAACAuvAfQawYt2rAZeW6AQZya6n/4wEAAAAwH2fsFXODTbqDkfrDPCsXQo9cHBk1YiOJ0koAAAAgdP4jiBXjgrbuYKjecDT1M99cAEdpJQAAABC2MCKIFeLKKHuDkbr9YfGzMAKnrEEgBwAAANQBgVzFJksrQ8vIud64ZiOM4wEAAAAwW+L7AFZNWVrZHymN80AuhGEnEqWVAAAAQF2EEUGskLK0chhgj1wRwK0RyAEAAABBIyNXsWxmRi6MwMmVVJKRAwAAAMIWRipohYynVo7UGw6nfuZbsxx2EsbxAAAAAJiNM/aKTQ476Q6K0so4jD9DRo8cAAAAUAthRBArJGuM98i5QC4LJAPWbEQyJpzhKwAAAABm44y9Yi771h2M1AssI9dsxMqSSMYY34cCAAAAYIEwIogV4rJvvYnSylB60s6vZzq/nvk+DAAAAABHYGplxbJ4YiF4mZELoyfth9/xVfr+tz7s+zAAAAAAHIFArmLTGbnh1M98a2eJ2hlPCQAAACB0YUQQK2TcIzcMrkcOAAAAQD0QQVQsiowasZkurWRKJAAAAIATIILwIEviqWEnjPsHAAAAcBJEEB5kSVSWVkZGSiitBAAAAHACRBAepEmkbj8fdpIlYUysBAAAAFAfBHIeZEmk3jDvkaM/DgAAAMBJEUV4kCVxkZEb0R8HAAAA4MSIIjxIJ3rkyMgBAAAAOCmiCA9caWV3SCAHAAAA4OSIIjwoh530Rww7AQAAAHBiBHIelMNOyMgBAAAAuAtEER6Uw076Q4adAAAAADgxoggPymEnQ6ZWAgAAADg5oggPsiRSb+B65PgTAAAAADgZoggPskak7oAeOQAAAAB3hyjCgzSO80BuMFIa8ycAAAAAcDJEER5kjaK0cjBk/QAAAACAEyOQ88CtH9jvU1oJAAAA4OSIIjxwwdud7oBhJwAAAABOjCjCA1dOORxZMnIAAAAATowowoPJLBw9cgAAAABOaqlAzhhz1hjzUWPM08W/Z+bc7rIx5peNMZ8xxnzaGPOKZe637iazcGTkAAAAAJzUslHE+yU9Za19VNJTxfez/Jykn7TWvk7SY5JeWPJ+ay0jkAMAAACwhGWjiPdIerL4+klJ33nwBsaY10tKrLUflSRr7R1r7e6S91tr06WVBHIAAAAATmbZKOI+a+1VSSr+vTDjNq+WdMMY80vGmE8YY37SGLPSjWGTfXFk5AAAAACcVHLUDYwxvyLp4oxf/cQJ7uNbJL1R0hcl/YKkH5D0MzPu632S3idJly9fPub/fP2QkQMAAACwjCMDOWvtu+b9zhjzvDHmkrX2qjHmkmb3vj0j6RPW2t8v/jv/SdJbNCOQs9Z+UNIHJenKlSv2eP8X6iclkAMAAACwhGWjiI9IeqL4+glJH55xm9+QdMYYc774/lslfXrJ+621ydJK1g8AAAAAOKllA7kPSHrcGPO0pMeL72WMuWKM+ZAkWWuHkn5M0lPGmE9KMpL++ZL3W2tZg6mVAAAAAO7ekaWVi1hrr0l654yff1zSeye+/6ikr1vmvk6TNCaQAwAAAHD3iCI8mMzI0SMHAAAA4KSIIjxg/QAAAACAZRBFeDA9tZJhJwAAAABOhkDOg8lySjJyAAAAAE6KKMKDJDKKTP41PXIAAAAATooowgNjTJmJIyMHAAAA4KSIIjxxvXGTqwgAAAAA4DiIIjxxmThKKwEAAACcFFGEJ1kSKY0jGWN8HwoAAACAmiGQ8yRLIrJxAAAAAO4KkYQnaRIz6AQAAADAXSGS8CRLIgI5AAAAAHeFSMITSisBAAAA3C0iCU9SMnIAAAAA7lLi+wBW1dc+sKkL603fhwEAAACghgjkPPnxd7/W9yEAAAAAqClq+wAAAACgZgjkAAAAAKBmCOQAAAAAoGYI5AAAAACgZgjkAAAAAKBmCOQAAAAAoGYI5AAAAACgZgjkAAAAAKBmCOQAAAAAoGYI5AAAAACgZgjkAAAAAKBmCOQAAAAAoGYI5AAAAACgZgjkAAAAAKBmCOQAAAAAoGYI5AAAAACgZgjkAAAAAKBmjLXW9zHMZIx5UdIfVHy325Jeqvg+garxPMdpx3Mcq4DnOVYBz3PpYWvt+Vm/CDaQ88EY83Fr7RXfxwF8JfE8x2nHcxyrgOc5VgHP88UorQQAAACAmiGQAwAAAICaIZCb9kHfBwBUgOc5Tjue41gFPM+xCnieL0CPHAAAAADUDBk5AAAAAKgZArmCMebdxpjPGmN+1xjzft/HAyzLGPOQMeZXjTGfMcb8tjHmR4qfnzXGfNQY83Tx7xnfxwosyxgTG2M+YYz5z8X3jxhjPlY8z3/BGJP6Pkbgbhljtowxv2iM+Z3iPf2tvJfjtDHG/MXifOVTxph/Y4xp8l6+GIGc8hMASf9M0rdJer2k7zXGvN7vUQFLG0j6y9ba10l6i6Q/Xzyv3y/pKWvto5KeKr4H6u5HJH1m4vu/L+kfF8/z65L+jJejAu6NfyLpv1lrXyvp65U/13kvx6lhjHlA0l+QdMVa+zWSYknfI97LFyKQyz0m6Xettb9vre1J+reS3uP5mIClWGuvWmv/b/H1beUf/A8of24/WdzsSUnf6ecIgXvDGPOgpD8q6UPF90bSt0r6xeImPM9RW8aYDUlvk/QzkmSt7Vlrb4j3cpw+iaQ1Y0wiqSXpqngvX4hALveApC9NfP9M8TPgVDDGvELSGyV9TNJ91tqrUh7sSbrg78iAe+KnJP24pFHx/TlJN6y1g+J73tNRZ6+U9KKkf1mUD3/IGNMW7+U4Ray1z0r6B5K+qDyAuynpN8V7+UIEcjkz42eM88SpYIzpSPoPkn7UWnvL9/EA95Ix5jskvWCt/c3JH8+4Ke/pqKtE0jdI+mlr7Rsl7YgySpwyRY/neyQ9Iul+SW3lLU8H8V4+gUAu94ykhya+f1DSlz0dC3DPGGMayoO4f22t/aXix88bYy4Vv78k6QVfxwfcA98s6Y8bY76gvCz+W5Vn6LaK8hyJ93TU2zOSnrHWfqz4/heVB3a8l+M0eZekz1trX7TW9iX9kqRvEu/lCxHI5X5D0qPFZJxUeXPlRzwfE7CUok/oZyR9xlr7jyZ+9RFJTxRfPyHpw1UfG3CvWGv/mrX2QWvtK5S/d/93a+33SfpVSX+iuBnPc9SWtfY5SV8yxrym+NE7JX1avJfjdPmipLcYY1rF+Yt7nvNevgALwQvGmG9XfhU3lvQvrLV/z/MhAUsxxvwhSf9L0ic17h3668r75P6dpMvK3zj/pLX2ZS8HCdxDxpi3S/oxa+13GGNeqTxDd1bSJyT9KWtt1+fxAXfLGPMG5cN8Ukm/L+lPK78Yz3s5Tg1jzN+W9N3Kp25/QtJ7lffE8V4+B4EcAAAAANQMpZUAAAAAUDMEcgAAAABQMwRyAAAAAFAzBHIAAAAAUDMEcgAAAABQMwRyAAAAAFAzBHIAAAAAUDMEcgAAAABQM/8fJYZIQHIQvWoAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 1080x540 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=[15, 7.5]); # Set dimensions for figure\n",
    "plt.plot(data['data'])\n",
    "plt.title(\"Log Difference of Quaterly EPS for Johnson & Johnson\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_pacf(simulated_AR3_data);\n",
    "plot_acf(simulated_AR3_data);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "rho: [ 0.68878493  0.44183118  0.40543803 -0.39895857 -0.18705244]\n",
      "sigma: 0.1093648131173019\n"
     ]
    }
   ],
   "source": [
    "# Try a AR(5) model\n",
    "rho, sigma = yule_walker(data['data'], 5)\n",
    "print(f'rho: {-rho}')\n",
    "print(f'sigma: {sigma}')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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